Big country
TGT Addict
You can also opt for the 204 for deer if you want to put the time in to master that weapon to point where you can shoot the eyes out of flies at 200 or so. Shot placement is key. I wouldn't try a 204 on a hog, but I'd have no problem talking deer with it. My cousin used a 222 on deer and it did great. I know people that use a 257 or other quarter bore's for everything they do.I don't understand the recoil excuse. In hunting you are taking very few shots, and honestly you don't feel the recoil. I've shot .22 LR to .460 Weatherby Magnum, and would feel fine with either.
If you are "recoil sensitive" then opt for a heavy gun in a .30-caliber bullet, or a light gun with a .243 / 6mm bullet. In Texas you can get away with just about anything on most of our game. We just got back blowing up small varmints with a .204 Ruger.