You all don’t need me! You’ve got this!
In a state that does not have friendly firearm laws, I would be very hesitant to carry anything that resembles a firearm even if it wasn’t a “real” firearm (pellet gun, bb gun, squirt gun that looks like a “real” gun).
Even in states where I can carry, I would do everything I could to avoid shooting a dog. People are incredibly attached to their dogs (“fur-babies” check out this thread: Self-defense against a dog). Shooting their dog will cause issues, even if they were in the wrong.
I have a pit bull and I let her out to do her business without a leash in my yard (no fence). However, she is well trained and would rather lick you to death than bite you. That specific breed gets a very bad rap. 
This is what she does 99% of the time outside (when she’s not doing her business:
