I'd take a very sharp knife (x-acto knife, razor blade, etc) and cut off any loose burrs, then polish and burnish as Velognome described.
I've done exactly this before. A couple applications black shoe polish, really rubbing it in and letting it sit, got the damaged part to the right color.
I've also done the same thing with a nice pair of black dress shoes I scraped up really badly in a motorcycle crash. Fortunately for the rest of my body, I was wearing a snowmobile suit over my monkey suit when I went down.