Answer is state specific. Here is a link discussing Texas law. No statute authorizing deadly force against dog for human attack but permitting deadly force to protect your animal! You would have to rely on the common law (no statute) of "necessity" as to the attack against the person.
Can I be Arrested for Shooting an Attacking Dog in Texas? - U.S. & Texas LawShield For dog walking I carry a .22 revolver and would go for a shot in the hip or shoulder first if I could. If this didn't discourage the attacking dog I will get serious. I don't want to kill the dog or injure it so as it has to be put down if I can avoid it.
OC spray would probably be more effective against an aggressive animal than a .22 revolver, especially a larger beast. Less liability as well.
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