Sounds like what might work for you is a Model 31 or Model 30. These were J frame (originally I frame) revolvers in .32 S&W Long with either 2 or 3" barrels. I have a 31-1 3" SB. They're about the same weight as a Model 36, maybe a tad lighter, but I don't have a postal scale handy. Certainly lighter than the beefy Ruger by, I'd say, around 6 to 8 ounces if memory serves.
You can get decent penetrating .32 S&W Long ammo from a number of sources, even the old factory RNL will poke a hole, but Georgia Arms sells light JHPs and a heavier flat point. You can also fire .32 S&W (not long) ammo in one. You can also use light kicking wadcutter ammo. These guns - and the cartridge itself - tend to be extremely accurate.
These guns sell for less than comparable .38s, and you should be able to get one for under 400.
I'd take one of these over a .22 LR gun any day of the week - bigger hole and you have more reliable centerfire ammo and not buggy rimfire ignition.
Try the Classifieds, Gunbroker, Auction Arms, etc.
Older Colt D frames in .32 can also be had, though in some cases you'd have to get the barrel cut from 4" down to 2".
If you get one of the J frames, Crimson Trace grips are of course an option.