Some would not mind marking up a board.
I do not agree with the mandatory surfacing part of this variation. Some subs remained virtually undetected on their voyages in the war. But the best way to win is to use them
(make them appear.)KILL!
For #s on the szs (sea zones), he/you could use
1) labels that can be purchased at any office supply store, or
2) a clear plastic sheet with the #s written on it and board corner marks (on the plastic) to know where to situate the sheet over the board, or
3) a masterlist of sea sones.
I've used, and currently have some on my board, Avery brand 1/4" round color coding labels which come in a roll. They are very small and can be ignored if you want to play a regular game between trial runs.