Chicken wire only keeps chickens IN, doesn't keep predators out. That is the weakest link of your coop. Oh my yes, coons can climb, and they are persistent and smart - they can figure out how to get into anything unless you stop them. I wouldn't use straight peroxide, it burns tissue which sure doesn't help healing. You could get an oinment like polysporin or bacitracin (or combination) if you don't like neosporine. Just don't get anything with 'caine" in it (as in benzocaine, etc.) as a painkiller I've heard it is very bad for chickens.
Your single winger sounds like a real plucky gal. Good for her, I hope she will continue to do well. It's amazing what chickens can overcome.