The primary role of your "non-dominant hand" is to steady the handgun for the shot rather and help "control" the recoil rather than to "absorb" a lot of the recoil/torque
With the single-action revolvers (a la Ruger Blackhawk and Super Blackhawk) the design intent of the grip is to let the gun ride up in your hand and your hand ride up with the gun, and the challenge is more to control that upward motion - gripping the gun
so the motion is straight "up" rather than twisting up and to one side or the other. I happen to hunt with a Super Blackhawk (.44 mag.) with a 7.5" barrel. I'm used to it so it's fine. If I were starting over I would probably opt for a 5.5" barrel for carrying convenience and slightly easier control of the torque. I would never use any less than a 5.5" barrel length though because of the increased noise.
With double-action revolvers (a la the Smith & Wessons) the grip design brings the recoil "back" into your hand and, though it is somewhat more prone to causing a flinch to develop, it eases the torque control a bit.
Some people hunt deer and hogs with semi-autos. I never have and it doesn't appeal to me.
The Thompson Center Contender pistol is a different ball game. It is an excellent hunting weapon even though it is a single shot. But there are some caveats with it too. On the plus side - it is easily scoped, comes in mulitple barrel lengths, the barrels/calibers are interchangable, it is an easy gun to steady, once fired it is completely safe (single shot), it is hefty even in the more compact versions, it can use any bullet you can buy to handload, it actually
comes with pretty decent iron sights if you don't wish to scope it, and even better "irons" are commonly available for it. On the "not so plus" side - scope power is best kept to 4x or less, with less being better. But that is true with any hunting handgun. Scopes on handguns require focus and practice and they are not generally as fast with which to acquire the sight picture as irons. Some folks use the new "RedDot" style sights and they work well, at least at .44 magnum ranges. I have a less-expensive model on my G2 .22lr barrel and have shot 1-inch groups at 25yds. with it. Haven't tried paper targets any farther with it though.
The regular Contender frame and the G2 frame will host such calibers as .357 mag., .357 Maximum .41 mag,, .44 mag., .45 LC, the .45/70, the .223 Remington, and the 30/30, and all of those will take deer - the last three at greater range. These two frames fit me best because I have beefy hands and only average length fingers, so I can control the recoil well. The G2 frame is the newer, and better, frame of the two.
The new Encore frame hosts all manner of rifle cartridges including the .243, the .25/06, the .270, the 7mm-08 and others. These cannot be used on the regular and G2 frames. I got all excited about that caliber list until I picked up an Encore frame and found out it is too large to be a good, controllable fit for my hand. With further contemplation I remembered that my effective range would still be limited by the scope magnification regardless of the high-powered calibers.
From revolvers, I would stay with the .41 mag. and the .44 mag. I use .44 Special for practice and absolutely love it. I've never shot a deer with it and would avoid using it on deer unless the range was within about 40-50 yds. at most. No need to use it instead of the .44 mag.
In the Contender and G2, I would use either the 30/30 or the .223 with complete confidence to at least 150yds. The 30/30 -
with good bullets in handloads - to 200yds.
In the Encore frame - all the calibers wold do OK but will certainly be a handful even if the frame fits your hand well. I've shot the .243 and the .25/06 and they are "boistrous", to put it politely. And frankly, they would probably never be needed for deer, especially if one had a 30/30 barrel.
The single-shot nature of the Contender might seem like a negative but it really is not much of a liability at all.
Lovers of the .357 mag., and the .357 Maximum certainly take deer and hogs every year. I've shot woodchucks, song-dogs, and a couple hogs (very close) with the .357 mag but never deer and, since I am accustomed to the .44 mag, I probably won't ever try the .357. calibers.
HTH, Good Luck !