To augment the above list, here is my list of Civil War nurses who died after December 31, 1939 that I have found:
Katharina "Kate" Neale (née Dapp), age 91, who was born on July 4, 1848 in Balingen, Germany, and who died on February 1, 1940 in Portland, Oregon.
Harriet Brubaker (née Manning), age 95, who was born on October 7, 1844 in Fultonham, Ohio, and who died on February 6, 1940 in Saint Paris, Ohio.
Mary Elizabeth Osborn (née Carman), age 93, who was born on September 11, 1846 in Allegan County, Michigan, and who died on February 18, 1940 in Muskegon, Michigan.
Mary Elizabeth Miller (née Burk), age 97, who was born on January 27, 1843 in York, Pennsylvania, and who died on May 28, 1940 in Logansport, Indiana.
Mary Malissa Watson (née Busch), age 97, who was born on June 30, 1842 in Dayton, Ohio, and who died on June 26, 1940 in Dade County, Missouri.
Rosa/Rose Russell (née Gibson), age 94, who was born on December 20, 1845 in Warrenton, Mississippi, and who died on August 29, 1940 in Vicksburg, Mississippi. She claimed to have been 16 years older than that, but census records indicate 1845-ish is correct.
Mary Lovisa Catlin (née Osborn), age 96, who was born on May 13, 1844 in Canada, and who died on November 9, 1940 in National City, California.
Lurinda Caroline Smith (née Rollins), age 100, who was born on August 8, 1840 in Ducktown, Tennessee, and who died on November 22, 1940 in Jacksonville, Illinois.
Anna Howell Findlay (née Kennedy), age 88, who was born on June 28, 1852 in Hagerstown, Maryland, and who died on January 30, 1941 in Hagerstown, Maryland. As a young girl, she helped her mother nurse an injured soldier, Oliver Wendell Holmes, back to health. Wonder what happened to him after the war.
Eliza Pyle (née Stokes), age 96, who was born on January 13, 1845 in Rapahannock County, Virginia, and who died on July 9, 1941 in White County, Illinois. She claimed birth in 1843, but early census records indicate a slightly younger age.
Sarah Satirey Tooley (née McClaflin), age 102, who was born on March 18, 1840 in North Royalton, Ohio, and who died on April 13, 1942 in Valley City, North Dakota.
Alma Minerva McGowan (née Dent), age 102, who was born on September 30, 1839 in Rankin County, Mississippi, and who died on July 9, 1942 in Lovelady, Texas.
Sarah Matilda Vorus (née Strong), age 101, who was born on February 5, 1841 in New York City, and who died on July 28, 1942 in Billings, Montana. She claimed to have been a year older, but census records say otherwise.
Louisa Minerva Priest (née Chaney), age 99, who was born on October 31, 1842 in Tennessee, and who died on October 6, 1942 in Marietta, Ohio.
Lena Earl (née Pfeiffenberger), age 104, who was born on March 9, 1838 in Germany, and who died on January 20, 1943 in Riverside, Illinois.
Remita Amanda Rupp (née Robinson), age 88, who was born on January 19, 1855 in Egg Harbor Township in Atlantic County, New Jersey, and who died on March 12, 1943 in Darby, Pennsylvania.
Hannah Beavis Walters (née Randle), age 101, who was born on October 3, 1841 in Dartmouth, England, and who died on March 20, 1943 in Southport, England.
Mary Ann Jones (née Rickman), age 97, who was born on May 18, 1846 in Todd County, Kentucky, and who died on April 5, 1944 in Stanislaus County, California.
Mary Ellen Dubosq (née Carbin), age 92, who was born on May 9, 1852 in Philadelphia, Pennsylvania, and who died on June 11, 1944 in Delaware County, Pennsylvania.
Azubah Elizabeth Perkins (née Reddout), age 101, who was born on November 6, 1842 in Rushville, New York, and who died on July 5, 1944 in Park Ridge, Illinois. Oddly enough, she claimed to have been two years younger than she actually was in her later years.
Avice Ann Fisher (née Forrester), age 101, who was born on February 10, 1843 in New Brunswick, and who died on December 6, 1944 in Independence, Missouri.
Harriet M. Holmes (née Hinkson), age 102, who was born on July 29, 1843 in Worcester, Vermont, and who died on August 6, 1945 in Northfield, Vermont. She claimed she was born on July 28, but her birth record says otherwise.
Clara Helena Stuttz (née Thompson, but her original last name prior to coming to America was Vhertelle), age 94, who was born on November 1, 1850 in Berlin, Germany, and who died on October 4, 1945 in Toledo, Ohio.
Mary Courtney Ray (née Ward), aged at least 96 (but perhaps older), who was born on May 3 in a year no later than 1850 in Alabama, and who died on January 17, 1946 in Hinton, Oklahoma. A former slave, her age is all over the place in census records. When she died, her birth date was stated to be May 3, 1838 and her age to be 107, but the farther back in census records you get, the younger she becomes, before it stops at age 30 in the 1880 census. Her husband, Albert Ray, survived her at her death! A sergeant in the 44th United States Colored Infantry, he was born on December 18, 1842 in Alabama and died on March 20, 1948 in Hinton, Oklahoma, aged 105 (and his age is corroborated by census and enlistment records).
Emma Louise Nagle (née Becker), age 97 (or maybe 98), who was born on March 11, 1849 (or perhaps 1848?) in Philadelphia, Pennsylvania, and who died on November 26, 1946 in Bethlehem, Pennsylvania. She might have been a year older than claimed and born in 1848 rather than 1849, but I need to investigate further.
Mathilde Eleonora Adolphine "Pauline" Temme (née Dubrock), age 99, who was born on November 1, 1847 in Minden, Germany, and who died on May 30, 1947 in Wilkinsburg, Pennsylvania.
Susan C. Clayton (née Haines), age 96, who was born on September 13, 1851 in Bethlehem, Indiana, and who died on March 7, 1948 in Medford, Oregon.
Lavinia Minton (née Mount), age 100, who was born on November 22, 1847 in Red Bank, New Jersey, and who died on May 28, 1948 in Highlands, New Jersey. She claimed to have been born in 1844, but early life census records don't support this.
George Whitfield Tyner, age 100, who was born on April 24, 1849 in Thomastown, Mississippi, and who died on June 24, 1949 in West Monroe, Louisiana. He is the only MALE Civil War nurse that I know of who lived into the 1940s. He was a courier for the 33rd Mississippi Infantry and also worked as a nurse for the local hospital.
Sarah Jane "Jennie" Overstreet (née Titsworth), aged at least 93, who was born sometime in February (we only have her birth month from the 1900 census) no later than 1857 (or perhaps a few years earlier) in McCracken County, Kentucky, and who died on February 13, 1951 in Cecil, Kentucky. A former slave, she boasted of the fact that she had lived her entire life in the immediate vicinity of Paducah, with the farthest she had ever travelled having been a single trip to Metropolis, Illinois. Her family said that their records indicated that her age was 109, but it's unclear what they based that on. Census records are rather inconsistent on her age, but generally agree she was born in the range of 1852-1857, with the earliest census she was enumerated in, 1870, recording her age as 13.
Sarah Frances "Fannie" Rockwell (née Pearce), age 110, who was born on October 25, 1843 in Richmond, Virginia, and who died on November 23, 1953 in Danbury, Connecticut. She claimed in her later years to have been a year younger, but the summer 1850 census lists her age as 6 (indicating 1843), and the 1860 census lists her age as 18 (indicating 1841). Her age of 110 years, 29 days is the greatest age attained by any veteran of the Civil War that can be substantiated by documentary proof from their early life. Many claimed longer lifespans, but hers is the highest that thus far has actually been proven.
Hattie Carter (née Robinson), age at least 103, who was born in August (we only have her birth month from the 1900 census) no later than 1852 in Richmond, Virginia, and who died on January 9, 1956 in Greensburg, Pennsylvania. She claimed to have been 122(!) at her death, but early censuses indicate she was born in the early 1850s, with the earliest, the 1880 census, indicating 1852. A former slave, she worked as a nurse and as a food/gun/ammunition runner during the Siege of Richmond. After the war, she married a Union veteran. After she became a widow, she married another one. At her death, she was a double Civil War widow and received a widow's pension.
There are additionally two unverified claims to have been Civil War nurses that I have been unable to fully investigate:
Louise McHurd reportedly died on June 22, 1941 in Michigan. Jay Hoar says nothing else other than that about her in his table of Civil War nurses in a book he wrote. I have found no documents or census records for her. He might have gotten her name wrong.
James "Jim" Jones claimed to have been born sometime in November of 1835 (I can't find his actual claimed birthday) and died on December 8, 1950 in Jacksonville, Florida, at the claimed age of 115. He reportedly worked as a nurse in several hospitals in Jacksonville that were churches temporarily converted into hospitals for the duration of the war. I have found no documentation for him because his name is so common and the newspaper articles I have found don't give a lot of details about his family or where he was from.