Update: OP, I don't have pictures (sorry), but the paint I ordered was a pretty decent match. A bit too dark, but what I did was apply the paint with the included brush, then dabbed the excess off with a rag. Repeated this process for a few coats. Now the mark isn't noticeable at all unless you're really looking for it. I'm very happy with the result. I've already forgotten it's there.
Yours could be a little bit more tricky given it's not a rash right on the edge of the rim like mine was, but take your time and it'll look a lot better.