I know I am not in your area, but rather than shooting someone with an air pistol and really ticking them off, it sounds to me like he needs to learn to defend himself and stop the situation the right way.
For the open carry debate of an air pistol? He may as well carry a cap gun... and I am not sure about your state laws but if conflict did happen again it would be easy for the bully to mash him like a bug when he has the bat that was mentioned.. just a simple statement that he attacked the bully with a bat and the bully defended himself woud be really easy considering the situation.
Bully's need to be put in check.. but I am not sure that "appearing" to be packing is the right angle.
I OC'd before obtaining my concealed permit.. and still will on occasion when it is comfortable todo so versus concealed.. but open carrying a firearm.. I hope.. is not being driven by people who want to appear superior because they are carrying. That is the wrong reason to carry any weapon openly.
I dealt with being picked on a lot growing up... we didn't have nice clothes and nice shoes and we did not have the nicest things... people are mean and cold hearted and will beat someone verbally until they are down.
Maybe your friend would be able to purchase a less threatening self defense device for actual use on his attacker.. are stun guns and pepper spray legal there? Those should be able to be concealed in a pocket, and if not - mabe in a small pouch. That may keep the bully off his back once he gets a small taste of that spray/stun.
I am not an attorney, not am i familiar with state laws or local law in your area.... but just trying to mention a few other options.
Sometimes the appearance of being dangerous is not enough... big guys get robbed too.. god bless!