First, this question is both stupid, and incredibly great. I believe you could do that, IF you also mutated the beaver with spikes so it was very intelligent. Otherwise there is only one other way it could be an evil beaver overlord.
If ruin took over a beaver it may very well become a sort of creepy super-inquisitor, but as a beaver so full of spikes it would look like a walking pincushion. It is possible it would turn good though, and become a hero. I can see it know 'Mistborn: The Beaver Rises'.
Also, what would happen if a beaver (or other non-human species) took up a shard? Would it become enlightened, and become intelligent? Or would it stay and animal, causing chaos with it's huge levels of power?