SF,
If you have caught beaver then you have skinned them, that front foot you can snap with one hand. Sometimes if i dont have enough water to drown i will sill use a drown rig to get them out into the water where they cant tangle up. i've caught a few that other guys have lost that are missing front feet.
if you have box swivel on the end of your trap and trapping wire there is no investment into a drown rig. tie bag of rocks to wire, toss in deep water, pull wire tight and cut off so you have enough to stake at bank. holding the trap chain by the swivel,run the wire through the little hole in the end of the box swivel so the wire goes from bottom to top. (hard to explain but you will know if you got it right it will slide down but not back) then wire off to a stake on the bank. i prefer cable but would not hesitate to use wire again if i didnt have a cable rig with me.