I try to never skin a beaver ,the same day I catch it.They bleed profusely from the head,when fresh.I put newspapers or cardboard on the eloor,where it is nice and cool.I then lay the beavers on their backs,on the floor.I will leave them like this for a day or two,then skin.The paper helps absorb the water and the blood in the head coagulates.You then have a fairly dry,bloodfree pelt.
In all the years I have been taking beaver,I doubt if I have had a handful that had fleas .I just went ahead and skinned them,then put the pelt in the freezer.
Tom