Main Point - Accurate statistics about how many carried a pistol regularly , or semi regularly do not exist , much less What each of them carried .
To a partial extent , production figures , and ammunition catalogues can give an approximate guess at what in circulation , and in use in certain eras .
You are framing. Your inquiry from revisionist 20th Century viewpont . A more relevant period correct inquiry would be along the lines of : What handguns were carried , or kept reasonably at hand of medium or large size or caliber , with intentions of potentially use for a serious purpose , in percieved occasion of possible need .
Even with my revised parameters , it would be somewhat revisionist to make a cut off of .36/ .38 bore size , as .32's were common , and regarded more favorably then than today . Warm up out of the way , some catagories :
Cap & Ball - They didn't disappear. They were just as effective as every , many people already had them , or the used/ surplus cost was a small fraction of a new fangled cartridge gun .
Colt and Remington factory records exist of total production of Colt Army , Navy , and Remington New Model Army , New Model Navy and millitary purchase contracts . Some more digging of Military records should have at least some partial numbers of guns subsequently battle losses , unservicable , and sold as surplus . Plus post War Colt production .
Conversions of C&B , plus Transitional variants ( ie the Remington 1868 Cartridge gun predated the Open Top Colts , much less the SAA . Factory ammunition for the .44 Remington and .44 Colt cartridges continued well into the 20th Century
" Bulldogs " -Generic nicknames for buncha British and British inspired guns . Actual Webbly calibers include .44 , .442 , and .450 , which then and now would be considered reasonably powerful rounds . In addition to actual Webbly , countless millions of such guns were made in Europe and US , ranging from servicable clones to total junk .
American Pattern DA Revolver ( other than initially mentioned No 3 Variants ) -
S&W introduced the .38 S&W in 1876. It was considered a reasonably serious cartridge , kind of midway between mid 20th Century opinions of .38 Spl and .380 . S&W made a lot of them ( probably more in .32 than .38 , you can each decide how to classify .32 ) . Plus a plethora of mfg , made millions of both Top Break and ( non swing out) solid frame copies and knock offs , both with stubby bbls , and long bbls for belt use . Millions .
And as to the Wildness of the Wild West? Big cities on the coast , and Midwest as a whole had much higher violent crime rates , than the Western Frontier as a whole.
Heavily armed rough & ready frontiersmen , scuffing with each other , and organized and semi- organized groups of them violently taking on other loose groups ? At lot more of them by numbers in the Southern Appalachian region than out West .