In Elmer Keith's volume Sixguns, he relates his experience from both of the cavalry officers who were from both sides, the 1851 Navy and guns patterned on it were most likely used by both sides and regardless of rank, many line soldiers carried revolvers as well for back up.
Cap and ball is indeed fun, the cleaning may be a chore. I have heard of removing the wood and immersing the dirty revolver in mineral spirits, perhaps in a G.I. ammo can, this would allow the spirits to penetrate and soften the crud and also eliminate the oxygen that would cause corrosion, take it out, blow it out with compressed air, put the wood on and go shooting.
I have some foam gun cleaner, I like to spray the internals and leave that coating of gun cleaner protection on it, then go shooting, I believe this would be a great help in cleaning afterwards.
Brake cleaner is the same stuff as Birchwood Casey's Gun Scrubber, don't use the "environmentally safe" stuff, use the original stuff with ALL the nasty chemicals that make it work, scripture says we are getting a new heaven and earth anyway.