"Beaver
May be hunted and trapped, without a licence and during all seasons, on privately owned land by the owner or occupant of the land, or by a resident with written permission from the owner or occupant of the land."
https://mywildalberta.ca/trapping/re...-wildlife.aspx
Why not see if there's a trapper in the area who'll manage the beaver population for you? That way he'll utilize the entire beaver and it won't go to waste. Where are you located?