I think I wouldn't attempt removing the fly yourself. imagine fighting a 40lb water rat that uses his teeth to bring down trees, just to save him. If you call ASRD I'm sure they'll say "thanks, we'll look into it." and then nothing. If not ASRD who would you call?
Nature has a way of figuring things out. I've seen 3 legged, 1 eyed mammals many times thriving in the wild. The hook will most likely fall out in a few days, or the beaver will suffer adverse effects and feed a hungry coyote.
I personally feel bad for you Scel, a double articulated streamer gone.... ouch