Speaking for myself, a hunter in the thick timber and harwood creek bottoms of South Arkansas, all a handgun does is get in the way. It's so thick that it would be very easy to have a vine yank your pistol out while in hot pursuit of a thicket buck.
You need to look at a shorter rifle like a Marlin 30-30 or Remington Model 7 that can be quickly manipulated for quick shots on a wounded deer. I a have hunted for 29 years since the of 7 and I have never had the need for a handgun as backup. All it does is create excess baggage and I love handguns!
Forget about shooting a huge cartridge. Consider a lighter kicking round like a .308, .260 Rem, .243 Win, 30-30 etc. that can be easily shot on the fly without knocking your head off. I learned this the hard way toting a 30-06.