Black powder firearms also do not require any paperwork, except in New Jersey. Can have them shipped to residential addresses too. They are occasionally bought by convicted felons who want to defend themselves but cannot possess regulated firearms.
I recommend .44 caliber cap and ball revolvers of the “Remington 1858” design. More robust than the Colts and the .44 is more effective than the smaller calibers in this case.
EDIT: You won’t be looking to spend top dollar for actual antiques, if that wasn’t clear. Modern functioning replicas, mostly made in Italy by Pietta or Uberti, are both available and reasonably priced.
3dp2a might be cheaper, I think?
Edit: Easier to find ammo for, too.
It’s a neat idea, but it seems pretty limited.
2 shot magazine and you have to re-pressurize the air tank after, what was it? 2.5/3.5 magazines? I forget, 5 or 7 shots and it’s done.
The capacity isn’t a big issue. It’s the accuracy that matters.
Those particular models are decent at hunting distances. Not so much at longer ones.
They aren’t meant to spray and pray, or even for sustained use. They’re meant for a specific use case.
They also, imo, aren’t great for the kind of game the pictures they use make it seem they’re supposed to be good for. Penetration just isn’t reliable, and falls off as the tank does. They’d be fine for some game, but you aren’t taking down a deer with them reliably, or similar sized targets.
What they could do, in the context of this community, is discourage long pigs in certain circumstances. Move in, set up, damage a few targets with minimum sound, move out quick. Would a suppressed rifle be better? Absolutely. But, as the title of the post indicates, it’s a workaround for when that isn’t an option.