Congratulations on your first beaver you've caught ! I liked skinning beaver on a old kitchen table that I raised up with some planks on the floor and two tarp straps one on each end to hook into the legs so when I got past them I could hook the straps hooks into the legs and have resistance when I pulled and skinned out the beaver .
I used a round table because that's what I had found at a thrift store .
And it's quick and easy to clean up when you're done .

I had them attached to a work bench that I'd slide the table under so to speak .it's fast and simple to clean up when done and then you can board the beaver on the table when finished .

Another though get a rubber mat to stand on while skinning it will help save your back .

Keep up the good work !!!!