I dont know about these guys but I am dumb enough to do something like that. I would leave my quiver full of extra arrows on there incase I put in a bad shot and get a pissed of beaver. Then you can shoot it again. If you can I think it would be easier to trap it. If a fool like me can trap them, then you surely can!
I just got my first one this winter, and I am currently taking care of the hide and tail. The tail is like pure cartilage, and fleshing that thing is a pain. I have done alot of different types of hides and a beaver in general is just kinda a pain. But it is worth it so far. I would say the best bet is to tan it . . . that will make it so much easier to work with verses air drying it, that and if you accidentally dont clear off enough tanning it will not stink like air drying. both will work though- Good luck!