Absolutely!
Guns were made to be shot, and chances are your Deringer was shot in the past. Previous owners just shot appropriate loads and cleaned it properly. There’s no reason you can’t do the same, and later pass it on to the next generation in just as good condition as it is now. We just try to be sensible.
I’ve seen old guns left in storage that were rusted and the stocks damaged by bugs or rot. Guns that get pulled out and shot, or even just handled by knowledgeable owners, seem to stay in good shape. Proper loads aren’t going to hurt them, and it takes a lot of shooting to induce any real wear. They get cleaned after shooting and wiped down after handling.
The last original I shot was an M1842 I.N. Johnson Dragoon pistol that I bought a couple of years ago. It was fun, and it didn’t hurt the gun one bit. I have an original Whitney M1841 “Mississippi” Rifle that will absolutely be shot. In my experience, original sporting and military guns, especially the locks, are built better than the mass-produced reproductions.
The only requirement around here is that after you shoot that pocket rocket, you need to post again and tell us about the experience.
Notchy Bob