Well, having no direct experience with corn injuries, I found a garter snake that had been run over with a lawn mower once and she had SEVERE damage near her head. I kept her in a small 5 gallon tank at the time (this is before I even had snakes of my own) and rinsed her wounds with peroxide- it fizzes and looks awful but it cleaned it out. I then treated it with neosporin daily and rinsed it out daily. She never had any issue eating, and when she escaped her tank I figured it was her way of saying "thanks, I'd like to go now".
With the injury being on the neck I would worry about possible punctures to the pharynx, so perhaps a vet visit is best before offering food? Like I said, I had no idea what I was doing with the garter, it just turned out well. I would also be worried about possible bacteria from the cat saliva. My first corn was killed by my cat, and I've heard that the bacteria kills birds, since birds=reptiles.. I'd be concerned.
