When I trapped hard, I skinned 160-170 beaver, 80-100 coon, coyotes, fox, otter, mink bobcats, and everything under the sun, and most of the times I had multiple catches of each critter with each trap set. I tried the air method once on a beaver and it worked great! 20 minutes after the hide was off, the hair slipped out, and ended up having a softball size bald spot in the hide. where the air was pushing the hardest, it ended up thinning the skin to much, which caused the slip.
Best method is knife that I have found for skinning animals for pelts, and doing a top notch job at it. Beaver suck, not other way around it, but the more you do them, the quicker you get. I can now skin a blanket size beaver in less than 10 minutes from start to finish, you just have to get your system down to do so.
I'll try and give a brief way of how I do it.
I start by having a sharp hachet, and chop all 4 legs off right at the long fur line. I then take a small skinning knife, and cut the hide away from the legs, in a circular motion. Basically going parallel to the leg bone, but not splitting the hide. Then I cut the tail off, split from behind the butt to straight up and out of the chin by the teeth. From there I just start peeling him down both sides. If you cut the hide away from the legs like I did before, the legs pop right out. Once I have him "halfway around", I flip him over and keep going. Once you get to the neck and head, just slow down and don't cut to deep. That is where the skin is the thinnest and you will cut holes in it. If you do, no big deal, once they take the hide for the final finish before it goes to garments, the head is cut off anyways.
Also, be very careful not to cut to the hide to hard, you will get what they call false knife cuts, which do not cut through the hide, but thin it. If you ever finish a beaver, you will see the pains of a false knife cut. The hide will tear there while fleshing, and the hair will slip from lack of skin to hold on to it.
If nothing else, bring it the classics and we will have a beaver skinning demonstration at the Outreach outdoors booth. :grin: