I've turned down lots of shots because I was uncomfortable about shooting at the range or for other reasons. Every time it happened, it was a reminder to me that I should do as the old african hunter said.
bring enough gun.
One thing I can assure everyone here of, you will never see a marine sniper passing up a shot because he brought a single shot .357. He will bring the best equipment, and he will "do his part" and he will take the shot, because that is the purpose.
Hunting, you go out to find the deer you want, and bring it home. If you find the deer and then don't bring it home because you deliberately handicapped yourself with a bow, that's one thing.
There's a point I'd like to make about primitive hunting. When I first went on a black powder hunt the rules were round ball and loose black powder. Now, we use pellets, saboted jacketed bullets, shotgun primers, etc. What makes the typical black powder shooter any more handicapped than a guy shooting a trapdoor springfield???
we used wooden laminated recurve 50 pound bows and wooden shafts, not the things used today.
There is honor in setting limitations and sticking in those limitations, and turning down the shot. There's nothing particularly impressive about shooting inadequate weapons and missing or wounding.