I still say there's no reason to shoot a dog (unless it's attacking someone).
There are plenty other ways to run it off your property. Hope you try the water hose on the next pup that might come along.
I don't use BB guns on pups. And by the time you get a hose and turn the water on, an unwelcome visiting dog will have done what it came to do. Get a stiffer backbone.
What if it threatens your livestock or chickens?