I've never tried it on wood but have tried it on other things and it works great. Lemon juice. Citric acid. spread it on and put it in the sun. Disappears, don't know where it goes, don't really care.
Citric acid is excellent, so is vinegar, so is phosphoric acid, which is specifically formulated get rid of rust. But nitric, sulfuric, etc. are all bad news, especially to skin!