In 1872 a new sword was prescribed for cavalry officers which was noticeably lighter than the model 1860 saber. The blade was much narrower, about 3/4 inch wide at the hilt, and the length of the blade was shortened to about 32 and 1/4 inches long. The length was on the order of a mounted infantry officer sword. I think cavalry officer swords tended to be at least 34 inches long, but officers paid for their own swords so there may have been some variation. Not all officers were the same size, so when dismounted there may have been a few short officers who would prefer a shorter sword. Swords were mostly badges of rank, even in the cavalry, and may not have gotten much use. In addition, many officers in the infantry or artillery preferred a cavalry style sword over the model 1860 officer's sword both during the Civil War and later. You can see that in photographs.
You can look up the 1872 cavalry officer's sword in Harold Peterson's "The American Sword 1775-1945." He has an example of the hilt and part of the blade by way of illustration. He mentions that the sword he shows was never sharpened and that sometimes these swords may have a ricasso of 8 or 9 inches. There is a single fuller on either side of the blade. In true Victorian Period fashion, the brass hilt is very busy with decoration. There are laurel leaves along the branches, there is an eagle holding arrows on top of the guard and a design on the bottom side of the guard. There is a fancy leaf and round structure where the knuckle bow attaches to the pommel and the pommel may have decorations such as a shield.
This was the 1872 officer's sword. There was no 1872 enlisted man's sword, well, no U.S. Army Model 1872 enlisted man's sword. There were so many left over from the Civil War that they didn't need to declare a new model, they needed to use up what they had. After the Civil War the cavalry didn't use swords much. For example, when Custer took the 7th Cavalry on campaign to the Little Big Horn in 1876, they didn't carry their swords with them. Peterson's opinion of the 1872 cavalry officer sword was that it was worthless, but not quite as worthless as the Model 1860 officer's sword. There were enlisted versions of the 1872 officer's sword, but they were non-regulation and probably were carried by National Guard units, state militias, and veterans' organizations. They are rather plain and look similar to you sword but where the knuckle bow attaches to the pommel they have a disk structure, mirroring the officer model but with none of the decoration. Needless to say, you don't see that many enlisted style swords.
I have to apologize; at this point I had intended to have illustrations of the 1872 officer sword and enlisted version, but I just can't put my hand on them at the moment. I have also been trying to get an example of the Horstmann enlisted cavalry sword similar to yours for a while. I might have one... somewhere. Usually I see them listed as Civil War Period, which they are not, for a lot more than I want to pay for what might be a 20th century, non-official U.S. sword. While I don't have any hard information on them, I believe they are post 1872 and might date to the 1890's or later. I have probably seen one with a blade marked, "GERMANY," which leads me to believe it was made after a Tariff was passed in the U.S. around 1890. It is not an officer sword, so not a Model 1872, and thus non-regulation. It is not the enlisted version of the officers' sword, so maybe not a militia or national guard but on the other hand, maybe it is. It's a tad short so maybe for a short cavalryman, but then maybe for a cadet in a military school. It's an interesting sword and a good example of what is not a Civil War sword. The fact that it is in relic condition makes it look neat and you could spin any number of yarns that could possibly be true for it to end up that way.
I also need to add my disclaimer that I am not an expert. I could be off on the identification (I wish I could find my example swords) although I don't believe so. If someone else has something to add, please do. There should be enough info in my responses that you could do your own research and see if you arrive at the same conclusion.