Years ago they were perfectly legal, and were used for target shooting and varmint hunting. Obviously to control the noise. Then the wrong people started using them for the wrong reasons (Mob, crime) and they ended up being outlawed pretty much. At least that is how it was explained to me.
And they are not illegal except in a few states, you just have to get a permit to use them. And in most states they are not legal to hunt big with. You can own them, the hunting regs just don't allow them is all. Same thing with using laser sights, they are not illegal you just can't hunt with them in most states is all.
I am going to admit something I shouldn't on a public forum but since there is no way to prove it anymore I don't feel too worried about it. I have messed with them, done a lot of research on them and even owned and made a few illegally. You can make a very effective one for pretty cheap if you don't care what it looks like or if you don't want it to last a long time. Some of the more expensive ones work better and last a lot longer though. And some that are made for specific applications actually reduce the velocity on their own so you don't need to switch to subsonic ammo.
Depending on how well made it is and how well it is fitted to your gun it could degrade accuracy as well. I don't believe for what you are looking at that will be an issue though unless the install is very poor.
I would love to use one for varmint hunting, but I don't think I would bother with it for deer hunting. Just me though. Ear protectors work just fine for me and I can get the foam ones at work for free.
And while they won't make a high powered cartridge completely quiet they will quiet it down quite a bit. Plus help with muzzle jump and flash. And like I said before while they still make noise it is very non directional.
My only concern with using one on a single shot pistol would be the weight and over all balance will be all messed up. It will have to be a fairly large one to be effective on that type of weapon. I assume you are using a scope anyway, because that will be a must as well. You may even have to mount it higher, I doubt it though.
If you can find some forums with more members from over seas, like remington girl said they use them quite a bit over there. I think rimfire central has a few members that use them as well.
Maybe some sniper forums wouldn't be a bad idea either.
If you get one let us know. And pics are a must

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Paul