Instead of searching for horse paint try dog grooming paint. Being an active member of the CKC we have titled many dogs and have used many products to cover up their little nicks and scars :) (we have miniature bull terriers so they tend to play rough!) lol I do not know off the top of my head any product that would match his color but there are TONS out there, there are chalks, sprays, paints.. its crazy! If I was you I would probably try putting some colesteral on the mark and then rubbing some dark brown show chalk on it..
Lol best of luck with this! And just to add no, I can't see them docking you marks in the show ring for this small mark :)
Here is a link to a place so you can just get an idea of how many product there are on the market: Dog Chalks and Powders at ShowDogStore.com