Its illegal to hunt deer with dogs in WI too. Dogs seen running deer CAN be shot on sight as well however we don't often see dogs running deer.
In regards to predators I'm all for their neutralization with extreme prejudice. In the protection of home, loved ones and property it is legal in WI to shoot predators (and scavengers such as coons) that are causing damage to your property. This includes feral cats, feral dogs, coyote and other critters (even including rabbits if they're raiding your garden).
If you're in the country side and shoot a predator/varmint that is damaging your property nobody's going to care. Simply shoot, shovel and move on. Nobody is going to call the police/sheriff.
If you're in a city you'd better be pretty careful about choosing to shoot a predator - most municipalities have ordnances against discharge of a firearm in city limits. If its truly a self defense situation you will most likely not be prosecuted however there's still a chance (depending on your DA and LEOs).
This is who we are, what we do.