Yeah. I'd try the ACV first. If the dog's been bitten, any of those other things will have a direct opening into the dog's body and soak it up. Those aren't exactly any benign ingredients in that ointment.
Piperonyl butoxide by itself can't kill anything, but it strengthens the reaction of other ingredients.
Cali considers Di-n-propyl Isocinchomeronate to be a carcinogen.
Pyrethrins from Chrysanthemums have a neurotoxic effect on insects, and can do the same to some pets.
Tell him to try mixing the ACV with some baby oil gel if necessary.