If you are using styrofoam, you'd want to use epoxy resin with fiberglass, which is not a health hazard unless you get to allergy levels. A sheet of Arborite or other countertop laminate is probably easier to get a good finish with, though. Coroplast would be easy, funky, and let you use thumb tacks instead of 'fridge magnets. Inside, the same material recommendations apply. A nice bead of caulking will make up for very casual joinry.
Or, how about gutting a bigger fridge, and slipping the shell over yours? Find your condenser, and its air supply, which should be left unobstructed, but it sounds like they may all be on the bottom, so you can do the back as well.
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