I've never had a dog kill any of my birds. That's because my property is fenced, my yards are fenced, and birds do not range unless I'm home. Since you can't shoot the irresponsible dog owner, it isn't the dog's fault and shouldn't be shot. The idiot owner will likely just buy another dog, and the problem continues. The dog is just being a dog. Nothing to debate there. SSS is parroted on here to sound cute, but it is a coward's way out, immoral, and most of all illegal. Surprised that tripe is allowed here.
I'd catch the dog. If the dog has tags with the owner's number, I'd call the owner to come pick up his dog. If not I'd call animal control to pick it up. Humane Society/Animal Control usually fines owners for that. If he comes over to get the dog, I'd have a witness with a camcorder when he shows up, get the camcorder going, and I'd warn him," This is the last time I will call you about this dog. If the dog shows up again on my property, I will surrender the dog to animal control, and you'll be in legal hell. Do you understand?" The chances are you won't see that dog again.
That so-called "ordinance" in your area sounds like BS to me. The OP needs to research that.