My great grandfather was from that era, mostly after the Indian Wars. He was a smallish, wiry little guy. He was not what I consider a 'cowboy', but was a 'mule skinner' and drove 8,10 & 12 hitches of mules pulling freight wagons.
I have found no references whatsoever of him carrying either a rifle or pistol. He may very well have. There ARE, however, several stories of his 'sorting out some difficulties' using his expertise with a black snake bull whip with which he was said to be an expert. He could, supposedly, flick horse flies off the mules without touching the mules.
I DO remember him and, though small of stature, would not have wanted to tangle with him.