As a bird dog owner can I please say...Be careful and make sure your traps are legally set. For the conibear, make sure it's either completely under water or is in a box set. I had to pull my dog out of one and was lucky to get to him alive. It was placed on Public hunting ground in Iowa and was on the land on a beaver slide, no box and full of musk. Luckily when he put his nose in his front paw was in as well, saved his neck from being broken and gave me the extra minute to open it up. I now carry a shoelace to open them up. Most dog owners I know are fine with trappers and we understand the risk when we run dogs, as long as the sets are legal and keep other users in mind. Leg holds pose no threat to dogs as we can quickly get to the dog, release them and usually just continue to look for Pheasant. So I prefer to see the leg holds.
Thanks for letting me spout off about the accidental trapping of bird dogs. If this is on private, posted land then by all means do what ever you need to get the beavers out.
Jim