An interesting thought, but where would the cutoff be I wonder...
That happens when shooting humans as well. The AZ law says you need a reasonable belief that your life is in danger, or severe bodily harm will happen. If it is a 100 lb girl faced with a 300 lb attacker with a knife, it is easy. If it is an older man confronted by a younger man the same size, armed with a small knife, then things get murky. Until one gets to court, you just do not know.
The only time I ever pulled a gun, I was alone, miles from the nearest road, and there were 8 guys moving to surround me. I had a 6 shot .22 that I pulled and got ready to use against the closest guy. They stopped trying to surround me, and I left. That was easy to decide. They didn't say a word, but there was no doubt I was badly outnumbered, and they weren't looking for advice on good trails for hiking!
Against one dog, I'd feel pretty comfortable taking one on unarmed up to about 100 lbs. Someone who hasn't owned dogs their entire life may have a different threshold. Against 2 or more dogs, I wouldn't hesitate to shoot a 50 lb dog. I don't want to wait until my hamstring is torn out to decide I needed more force.
Cruelty laws are intended to prevent the jerk from shooting dogs for fun, or making up an excuse, or chasing a dog down the street to shoot him. If a person shoots a dog in the chest or face while on his own property, and the dog is big enough to do actual harm, I'd bet no one would be charged. A DA filing charges in those circumstances would be in deep doo-doo politically. In Arizona, at least. Same for rural Colorado. Don't know about Denver.