[Arran]

If it were my set I would give it a good cleaning with some cream hand cleaner like GoJo first to get the dirt and filth off just to see what you have. If there are too many stains or spots where the old finish is lifting off I would just strip the cabinet and refinish it. It's nice to preserve an old finish when you can, but sometimes it's more effort then it's worth. I suppose you could touch up the cabinet in such cases but given the size, and the fact that it's a 1940s AC/DC set, you could easily strip and refinish the set withing a week with spray cans.
Regards
Arran