MEK is a bit more aggressive than acetone. Not nearly aggressive enough to affect epoxy inks and resins. Neither is THF; many conformal coatings happen to be susceptible to it though.
N-methyl-pyrollidone and DMSO may be less toxic (but more expensive..?) alternatives to DCM. Both absorb readily into the skin...
In any case, the substrate is epoxy too, so you can't let it soak, you'll just turn the whole board to mush. I would guess, wiping on some solvent, letting it soak in slightly, then abrading away that layer, and repeating until the mask layer is clear, is the way to go. Fiberglass brush is usually recommended.
Also, frikken lazers. Won't harm the copper, of course again you need to avoid damaging the substrate too deeply in the process.
Tim