I also prefer a double action 22 revolver over a single action due to handling the small cartridges.
The S&W M617 is a good choice. I would prefer the 4" for most shooting situations, but I don't hunt small animals with one either. In your case, I would choose the 6". It certainly would be a lot of fun.
I don't own a 617, but I have a number of M17's and M18's. Both 6 shooters.
A 5" S&W M63 (8 shot) might be a consideration (22LR). They haven't made them for a a few years, but they are very good small framed revolvers that to many feel more like a 22 should. The 3" is currently made. I have both the 3" and 5".
The old model S&W 48 was chambered in both 22LR and 22 mag. Some shipped with two cylinders. It would be a 6 shooter however, but still a double action. Probably would be fairly expensive if you found one.
If I were hunting them for fun, I would probably go with a Ruger Mark II or III Govt Model (heavy bull barrel) 22 pistol. They are very accurate. You can get these with a long barrel if you want.