The units named were exceptional. Taken as a whole, revolvers were always rather scarce in Confederate cavalry service. As time went on, shotguns and other privately owned arms disappeared, replaced by government-issued and captured infantry arms.
Govan enlisted at Holly Springs MS in February of 1863, as I recall. Rebel Raider: The Life of General John Hunt Morgan by James A. Ramage, includes this passage onpage 151 concerning conditions that winter.
In middle Tennessee, supplies became even more scarce; morale and discipline declined; and the effective strength of each regiment was weakened as the men roved about in search of food. The 2nd Kentucky, Morgan's original regiment and his favorite -- "my Regulars," he called them -- rebelled against conditions by refusing to carry their weapons. They remained in camp and answered bugle calls but simply fell in sans rifles. Various threats were made to no avail, but finally, when each man lacking a weapon was ordered to drill with a heavy fence rail on his shoulder, they "found" their rifles in a nearby farmhouse.
Ramage is quoting from Duke's history, pp. 404-05.
Armed as they were with single-shot weapons, Morgan's men were at a distinct disadvantage when involved in a mounted fight or attempting to escape on horseback, as at Snow's Hill, Tenn., Apr. 3, 1863, and again at Woodbury, Tenn., Apr. 19, 1863. Federal cavalrymen using sabers cut Morgan's helpless men to pieces.
Many officers, Morgan's escort and a few others carried handguns of different makes and models, but it is fantasy to imagine the typical Confederate trooper with a pair of Colt's revolvers.