I suppose the answer to this would depend upon what you regard as the period of the "Wild West". Accepting for a moment that in at least in Wyoming and perhaps Montana it ran nearly up to World War One, you do find the unusual example of the 1910 Sheep Creek Raid in the Big Horn Basin of Wyoming. One of the killers in that raid was identified simply because he went to the raid armed with a Remington Model 1908 semi automatic rifle and was known to be one of the few people in the area to own one, semi autos being unusual at the time. The cartridge, a .25 (or maybe .35) Remington gave him away given the number of expended cartridges that he left on the ground following the raid. That would tell us, as an example, that they were both known, but not terrible common yet.

See A Vast Amount Of Trouble by Davis on this raid and that topic. You might also consult Ten Sleep And No Rest.

FWIW, this is the same rifle depicted in Remington's famous "Big Enough For the Biggest Game" advertisement of the period.

By way of another example, when Tom Horn escaped from the Cheyenne jail with another prisoner in August 1903 he armed himself with a handgun from the jailer, but was captured quickly thereafter as he did not know how to use it. It was an early model of semi automatic pistol, although I've forgotten which one. Nearly any of the texts dealing with Horn mention this incident.

As for a "pair" of revolvers. Not likely. While multiple (two or even three) revolvers were quite common in the black powder era (see Firearms of the American West: 1803-1865 Book by Charles G. Worman and Louis A. Garavaglia) they were not when cartridge arms came in and you could reload them. Again, see Firearms of the American West, 1866-1894 by Louis A. Garavaglia and Charles G. Worman