22mag is a good choice, for sure.
So oos the Hoornet, havenn't used a 17 riimfire, but I'm sure it would be great, just watch where you shoot them, becuase a bit off on the head shot and he is gone with the smaller calibers!
I don't like shotguns for fur work, but I know some use them.
I have used reeduced loads from the Speer manual and cast loads from thhe Lyman for them in calibers from 25/20 all the way up to '06, and really liike useing my .58 Hawken with a 45 grain charge, but haven't shot a beaver with it for a few years.
One of the better know trappers up here uses a 25/20 in a Winchester Model '92 and really brags it up, but most uses a .22rimfire.
When my father was working in thhe ammunition industry , he told me that thee natives in northern Ontario and Manitoba liked the .22 short!
Cat