For years I carried a Ruger Mark I target model pistol (5.5" bull barrel) on the trap line. It was light and accurate as a rifle out to 50 yards (admittedly an optimistic distance on a trap line). Not so much to dispatch trapped animals (I hate to add bullet holes to a trapped animal), but more to collect small game I might come across and occasionally to take out a coyote or bobcat that was a bit "frisky" in the trap.
When hogs began to appear in our area, the .22 LR seemed a bit small particularly if the hogs were not trapped (yes, I did trap the hogs with snares). I began to carry a 4 3/4" barrel single-action in .45 Colt in a cross-draw holster on my left hip with the Ruger on my right side.
I'd sometimes compromise by carrying a 5 1/2" single-action in .32-20 alone instead of the Ruger and .45 (actually a bit small for hogs and a bit too much for small game, but it worked pretty much for everything if you were careful).
In truth, a handgun (or any gun) is not really needed on a trap line (or I should say is rarely needed)....but I've carried one so long I feel naked without something on my hip. I don't carry because I NEED it, I do so because I WANT to and can.
