Pembroke Welsh Corgi's are very good live stock guardians to chase off smaller predators such as foxes and below. They are also small, adorable, and low maintenance. I've kept them for yrs. Basset Hounds are no good haha. But honestly, no dog is going to work for a Mink. The best thing you can do is set traps and kill them. Or you will just have to put small enough wire around your pens that they cannot squeeze in. They can also climb very easily, so putting it just around the bottom won't work. Electric fence will work, I have pulled at least 2 minks off of my wire that was fried to it. I have a old weed cutter model that has a constant current...not pulse. I have wire ran around the bottom of my pens just 2 or 3 inches above the ground to keep from digging under, and I have another strand ran around the top perimeter to keep from climbing over and chewing through the netting. Minks are a terrible predator to deal with, they are too sneaky and quiet for dogs to hear until they are in the pen, then the dog cant do anything unless u keep it in the pen with the birds. You can get a small cage trap from tractor supply, and put some tuna fish or sardines in it, and I gaurantee you will catch it.