While I have never sold a beaver on the carcass, I sell a lot of them green,every year.
By skinning, you will keep a lot more of your freezer space,than carcassed beaver.This allows you to take more beaver at one time to the buyer.While some buyers will not buy beaver on the hoof--most will take them if they are skinned.
I flesh and stretch when I have time,but things are hectic--I just skin and freeze.
Tom