It's the old American tale again. A revolver is the thing that is needed. You can stick it in your belt, wave it around and show everyone that you mean business. The truth is a bit more disappointing.
Most revolvers at the beginning of the War were .36" or less and not very effective beyond 20 yards - 10 if you hadn't used one before (on a good day!). The 44 and 45s were the best at downing an opponent, but they did not appear until later. Trouble is, they were mainly a 'second arm' for cavalry, whose primary weapon was carbine or sword, and for those who were not issued rifles and needed something better than a sword for close-quarter defense. The line infantry HAD to have the musket or, better still, the rifle musket which had a much longer lethal range and, of course, a bayonet. There was no room for a pistol in your belt - it got in the way of reloading. It is not much of a defence against a company volley either.