I can't speak about the criminal types, but there's very little reference to hearing loss in the sporting literature from around this time. At this time you still had professional shooters who were shooting very high volumes of cartridges at game, so if there were noticable trends of severe hearing loss they probably would have written about. Though the guns of this era had a number of features that made them slightly more safe than modern firearms.

The first of these features is that guns of this era were largely using black powder. Black powder generates much lower pressures than modern smokeless powder, so you get much less blast off the muzzle as a result. Barrels on rifles and shotguns were generally much longer as well, which pushed the blast farther away from the shooters face. On firearms with shorter barrels like carbines and handguns, they were generally shooting subsonic cartridges which further reduced noise. While handguns posed the greatest risk to hearing, handgun shooting was not a particularly popular pastime and was mostly carried for protection.

Gunfights in the old west were relatively infrequent, even amongst the most famous gunfighters and lawmen, so even then the risk was low. Though the reality is the life of a famous gunfighter was usually a short one, so even if their antics would have lead to hearing loss they simply didn't live long enough for it to develop.