As someone who owns a partial, because my Ex knocked out two of my teeth, I would say I don't see how it could hurt. I use denture tablets on my teeth as well as my CamelBak reservoirs when they start to smell. The tabs that keep the partial lined up in my jaw are stainless steel, and in 4+ years, it hasn't done anything to them, nor has it etched the surface of the partial. I would say take the razor you have the least hope for, and try it out.
Originally Posted by gears
I think there are four items in this world that combined can solve any problem. They are: A pair of pliers, Duct Tape, paperclip/wire, and Barbicide.