Just bought a fab piece of 60s furniture from eBay. Unfortunately one of the surfaces must have been splashed at some point because it is covered in tiny black marks. It's over a large area. Would sandpaper work?
you will have to sand off the varnish, then you can bleach the stains with oxalic acid, which you can buy, in crystals, from specialist decorating shops. You may have to try ebay. It is poisonous. There used to be a merchant in my town that carried lines like gilding sheets and beeswax, so not at all mass market.
black water marks are often quite deep, so would need a lot of sanding otherwise.
you will need to sand and refinish the whole panel, or it would be patchy.