If you're going to use Nitromors, please read the instructions carefully. You ned to use Goggles/Eye protection, Gloves AND have the room well ventilated.
Yes, you can remove the stain/varnish (If it's plain, then try using a detail [or mouse] Sander - it'll be quicker, but there'll be more dust). Then rub the Wood with some White Spirit on a clean cloth (Going with the Grain), to get rid of the remaining dust.
I would recommend that you then use a water-based primer and then a water-based topcoat (Eggshell is the flattest of the three finishes. Satin would give a slight shine and Gloss is the most reflective). If they want a white colour, a water-based topcoat will stay white.