I cook and eat beavers that have been submerged under ice water for a week without any problems yet. It is Alaska, so the water is cold. Your mileage may vary. 
These beavers have been trapped. I cannot tell the difference between one I shot today and one I pulled up off the bottom that has been there all week. They eat the same and taste the same to me. 
I would think that you would get somewhere near that many days if your water is cold. I eat them all. 
Beaver Pot Roast and BBQ Beaver sandwiches are my favorites. 
Crock pot, cut up beaver, add bbq sauce and a little water, cook on low all day, pull meat off bone, add a little bbq sauce, jam it between some bread and you have a great sandwich.