Given the scope of the American Civil War you can say just about anything that happened and it probably did. Collecting shoulder straps or collar tabs from dead enemies undoubtedly took place. If I was writing an historical novel I would have a man do that, but I would have some of his mates criticize him and some envy his callousness. An officer might even berate the act. As for a primary or secondary account you will have to do your own research and we all would be keen to learn the result.
In my novel the sharpshooter would be a quiet lad, probably a hunter back home, tapped for his marksmanship. He quickly learns that the "rush" of the hunt when extended to his fellow man is irresistible. Add to that his rage against an enemy that has killed his friends and neighbors and I have a real killer. He measures out his powder and casts his bullets. He keeps his rifle spotless and the sights safely wrapped until needed. He collects his trophies when he can and secrets them in his haversack. Heaven forbid he gets captured.
The following seems to be the original letter Dwilma01's summary is based on, and it sounds as if the cavalryman was definitely interested in the shoulder straps. Certainly not a sniper, though, but at least it's an actual period example of someone trying to take shoulder straps as a trophy.
http://www.americancivilwar.asn.au/meet/2005_12_mtg_hore_ltr_trasc.htm
An officer by the name of Hansard, a first rate good hearted fellow, I should have liked you to have seem him Olivia a regular type of a South Carolina man with long hair flowing over his shoulders, a South man by birth but a good man for the Union, I think without exception the best looking man I ever saw, said: We will go together Harry, it will be safer". We rode along as fast as we could to the rear for we did not know how things were going on there, when just as we were thinking all safe, some of Mosby's cavalry that were scouting in our rear saw us and came down with a yell upon us. So thinking discretion the better part of valour, feeling quite confident that we should fall in with some of our Rear Guard in a few seconds I set Hansard the example of running away but he did not have such a good horse as mine and one of the Rebels was soon near enough to poor H. to call upon him to stop. He would not and the Rebel who was better mounted clutched at the bridle and then they had a struggle, their horses kicking, so that I could not get near enough to strike him well or shoot him with my revolver. He got the better of H. on the ground and drove his sword right into Hansard's chest. His horse had gone and he tore off his shoulder straps and shook them at me. I now felt as if he or I must be killed so taking a good aim at him, I had made up my mind I would kill him if I could I made my horse get so near that I was safe not to miss and I fired and dropped him dead, alongside poor H. This did not take 30 seconds, not near so long as it takes me to write. I sighted him along the barrel of my revolver and if I had not killed him the first time would have shot again for H. was a good friend to me.
Yes, and here is another example of souvenir collecting from a dead enemy. Although again, its not a Sharpe Shooter I had just recently posted this on another thread.
Death of Farnsworth as seen by William C. Oates, 15th Alabama.
" On the far right of the confederate line of battle, still held by Law's Brigade, one of the men in the 4th Alabama overheard two Yankee cavalry generals- Kilpatrick and Farnsworth - talking loudly in the woods. Kilpatrick was ordering Farnsworth to seize a North Carolina battery in rear of the Alabamians and the piece of intelligence allowed General Law to prepare for the attack. In a wild charge the Cavalrymen passed over the 1st Texas Lying in a skirmish line behind a wall. They then headed for the battery under fire from some Georgians, a cooking detail, and the 44th Alabama.
Oates received orders to move into the fracas as well, so he threw it out skirmishers and headed for the Yankees. As his man approached, one of the guns of the battery fired a shot of double canister and Oates remembered that the sound of the small lead balls passing over their heads reminded him of a covey of partridges in flight. Eventually, the officer commanding the cavalry was knocked from his horse with several mortal-looking wounds and lay on the ground awaiting death. A Lieut. Adrian, an officer of the 44th Alabama, was nearby trying to capture a horse and he accidentally found himself commanding Oates' skirmishers when the fuss broke out. He approached the dying Yankee, telling him, "Now, you surrender," figuring he had little choice in the matter, anyway. There were two different versions among the men as to what happened next. Oates said that the Yankee swore he would not surrender, and he turned his own pistol towards himself and pulled the trigger. Another story among the man said that he killed a Confederate who demanded his surrender and was shot by another. Whichever version is accurate, it left him just as dead.
Still exhausted, Oates saw the incident from about 50 yards away and one of his skirmishers after brought the dead soldier's shoulder bars to the colonel, saying "Colonel, don't you want the Yankee major's straps?" The mistake was an honest one- confederate majors wore one star on their collar- but the dead officer was no less then Brig. Gen. Elon J. Farnsworth. Oates went over to the body were squads of man had gathered to get their first look at a dead Yankee general. He found letters in his coat pocket addressed to "Gen. E. J. Farnsworth," apparently from the general's wife, and destroyed them out of respect."
Quoted from "Stand Firm Ye Boys From Maine: 20th Maine and the Gettysburg Campaign" pg 91-92
By Thomas A. Desjardin
I guess the best opportunity for a Sharpe Shooter to collect a trophy would be during a skirmish with the enemy in a quick retreat... Least that's how I'd write in up if I were writing a novel.