My 2 Cents
On a Primary Hunting Handgun a Muzzle Break is OK. You will probably be using hearing protection when shooting it.
In this application we are talking about a bowhunting backup handgun. You will probably need it in a hurry and not be in a situation to get hearing protection in play. This leaves out the really big magnums in my opinion.
This leaves the 41 Magnum, 44 Magnum, 45 Colt and handloaded 480 Ruger. Any of these should work well when properly loaded. This leaves picking what you want to shoot them in. I would probably go for open sights on a backup gun as well.