I used to carry a handgun every time I went hunting. Then it became obvious that that additional weight (especially if carried on the waist/hip) was simply too much for the big mountains. Changed over to a shoulder holdster and that helped but was still more weight than I wanted to deal with. It became painfully clear that as long as I had my rifle or scatter gun, no more be needed. However, that was with CF arms.
Only one time during a muzzleloader hunt I wished I had a sidearm. There were two Dobermans that came running up to me and began slowly circling me while growling, but they remained on opposite sides of me. I couldn’t keep both of them in sight at the same time even though I kept turning around. Knowing that if just one of them leapt at me, I would have been lucky to hit just one at such close distance and how quickly it most likely would have happened. So, I reached down and grabbed my hunting knife and held onto it tightly.
After about 3 minutes of that incident, and after I was loudly yelling at them, they finally headed out. After that, I gave the situation more thought of carrying a pistol during Muzzleloader season.
Since then, I decided that if I’m going to pack a pistol with me during a muzzleloader hunt, it’s going to be small and light. I did continue to pack a larger caliber pistol with me in a sidekick holdster every time I was up in the mountains, but only if I’m not carrying a rifle or scattergun.
In terms of finishing off a wounded critter, I can, and have, reloaded and did it right. I have also cut several deer's throats with my hunting knife but caution must be used. It can be dangerous especially if it has antlers.
By far the main reason why I’d want to pack a backup tool would be to protect myself from a couple of whacked out, two-legged creatures that might be insistent on doing me great bodily harm. I figure a small, light gut-buster will suffice.