Wax is difficult. Unless the wood is sealed, it gets deep in the wood. After adding wax, you cannot draw the lines any more - the ink/lacquer does not stick any more. So if you can plane the board, then first seal, then draw lines, then wax.
Always test the combination you intend to use with a test piece of wood, so you can see that the lines will be nice, and not smudging.
The Japanese use I guess some softer wax. I made mine with carnauba wax (which is the hardest natural wax).
I'd start by scrubbing down the surface with soap and water! Hopefully, you'll be happy with the amount of dirt that gets washed away. This is the way my current goban looked for several years before I gave it a wash.
The big stain came out and, after a little oiling, it now has a bright sparkle. I've washed other gobans with equally good results.
An amazing improvement, but it looks like lines were still good, but the original posters lines look worn off. Still it is worth a try to wash first as that is less drastic.