Blackpowder (replica antique) pistols are readily available in the US without any background checks. The last I checked, you can even purchase them by mail. And yes, provided you get one of a large enough caliber (.38 is bare minimum; larger would be better) they are definitely powerful enough to get the job done.
Their primary --and often overwhelming-- drawback, compared to modern firearms, is that they are more complex to operate and require considerably more training to use effectively. It is not as simple as dropping a cartridge into the chamber, cocking it, and pulling the trigger. You need to purchase bullets, powder, wads, and percusion caps separately --and you must know what type of each to use-- and then learn the skills to charge and prime the gun reliably.
If you don't mind learning a new skill, there's nothing against it as a method. In fact, it's probably significantly less expensive than any other firearm method. But it is complex, and --like any method-- it does require conscientious self-training to ensure any certainty of success.