Put plexiglas over the map. Leave the crayons in the box and write on the plexiglas with overhead projector pens.
I've found that Vis-a-Vis brand wet erase pens work best for these games. They don't smear like white board pens and easily clean up with just a wet rag.
They do seem to do a good job of staining finger though, so you might not want to use "spit and finger" to make minor track corections.