Is it possible to use nail polish remover or alcohol on a snowboard as a wax remover?

No, you could dissolve or scar the finish. You can use lighter fluid, if you can find it. They used to sell small yellow cans of it pretty cheaply in drug stores (with the cigars and cigarettes) or in tobacco shops. It will dissolve paraffin waxes safely but it is flammable so use it outside or somewhere with good ventilation and no flames or sparks. Just squirt it on a soft rag (old teeshirts work well) and wipe off the wax.

Yes, but neither is a good idea. The alcohol will probably not effect the wax. The nail polish remover may cut the wax but may also harm the board finish. The other ideas should be tried. Your best solution is to buy a commercial wax solvent. Visit your local Pro-Shop and inquire about their methods. Be sure to try the solvents on a small area to be sure it does not affect the board finish.