Melissa, there are proper paint strippers that are specifically for softening varnish, usually available anywhere that sells paint. You will also need a blade from a Stanley knife and some 80-grit or finer (bigger the number, smaller the grit) sandpaper, safety glasses and rubber gloves (paintstripper is corrosive) and a couple of brushes to apply the stripper. In a ventilated area.
Processes that have worked for me are:
Don't remove anything except the belly varnish, the sides and back make the job tedious, and achieve little acoustically.
Mask around the guitar with plastic electrical tape and polythene to prevent paintstripper 'fingerprints.'
Apply stripper and give it time to work. Remove softened varnish with blade, trying not to gouge. Use a big artist's brush around the awkward places, it will probably take several attempts to get all the varnish completely off.
Neutralise the stripper according to the instructions on the tin. Probably sponging with water.
Allow to dry thoroughly.
Sand if neccessary ONLY in the same direction as the grain. Use the sandpaper wrapped around a block, cork or rubber. DON'T use the sandpaper just with your fingers, unless you know exactly what you are doing.
Thin the varnish to the recommended maximum.

I'm only giving this advice because you are obviously determined to take the job on, I actually recommend that you buy a better box in the first place.(:<))