While I have hunted alot of small game with .22 handguns, I have always felt them to be very marginal on anything larger than rabbits. On raccoon, groundhog, wild turkey, opossum, porcupine, fox, trapped bobcats, fer4al dogs and coyotes the .22 LR is feeble. A .32 ACP with FMJ loads does just as well, which is faint praise indeed!
The .22 WMR with JHP loads is better than the LR for varmints, but even with FMJs ruins too much meat for eating game, and the ammo is very expensive. It's cheaper top reload .32s, they are more effective, and your pockets will still hold alot of them. Leather .22 cartridge loops can be "stretched" to hold .32s if you are patient, and they will hold rounds snugly.
If you do use a .22 LR for game, be sure to want to get one of the Hanned SGB dies to make your own flatpoint rounds. Penetrate better than HPs and better killers than LRN.
The .32 H&R Mag. Single Six with either .32 S&W Long "+P" reloads or .32 H&R Mags. is just about ideal as a small game, varmint, plinking and trail gun. It's a shame that they don't sell the adjustable sight version anymore. Mine shoots like a rifle out to about 100 yards. I find it no problem to hit a 5" steel auto popper out there. I use driving range pickup gold balls as practice targets, heaving them out by hand for the firt shot and see how far I can drive them out with a cylinder full. In good light with the best loads you can hit them at 50 yards about half the time.
With proper loads ballistics are equal to the .32-20. Look up my Gun Digest article several years back for a full explanation.
I use mostly .32 S&W Long reloads, because I have other handguns and now a rifle also in this caliber, and I want ammo to be interchangable in all. The general purpose small game and plinker is the 95-gr. Saeco #325 miniature Keith-style SWC in Remington .32 S&W Long cases with WSP primers and 2.5 grs. of Bullseye for about 850 f.p.s. in a 4" barrel.
This is a wee bit above published maximums, but this load is safe in my S&W Model 31, Colt Officer's Model Target, H&R 732 and the Single-Six. The "+P" load is 7 grs. of #2400 with the same bullet changing to the Federal 200 small rifle primer for 1080 f.p.s. I don't shoot this load in the H&R, but it is fine in the S&W 31 and the Colt. I also use this charge with the 85-gr. Hornady XTP hollowpoint in all the guns but the H&R.
Maximum effort load for the .32 H&R Magnum is the 85-gr. XTP with 4 grs. in .32 S&W Long cases or 5 grs. of W-W231 in Federal Magnum cases with the Federal 200 primer for use in Ruger and T/C handguns only, good for 1300 f.p.s. in a 4-5/8" barrel! I pressure tested these when I worked at Ruger. Both exceed SAAMI pressures for .32 H&R Mag, but are within the design limits of the Single Six at about 30,000 cup.
In the H&R and any other .32 S&W Long or H&R handguns not listed DO NOT exceed 3.5 grs. of 231 with 85-gr. XTP in S&W Long cases or 4.5 grs. in .32 H&R Magnum cases, which will approximate factory .32 H&R Mag. ballistics. The 3.5 gr. load in S&W Long cases is fine in post-war Colt Police Positive .32 NP, but shouldn't be used in older pre-1957 S&W .32 Hand Ejectors. The 4.5 grain H&R Mag. load is safe and accurate in the H&R revolver.