Could you take a picture and post it here for a look at this contraption you have. I'm sure that there are 120 volt wires feeding the coil and a multimeter would be helpful in determining which exact wires those are. But I would love to see a picture, it would help a ton in figuring out what you'd need to do to install a regular GFCI in this location.
Oh, and if you feel like paying $5.00, the link below says they have the instructions for converting your razor-only receptacle to a GFCI type.
http://www.electrical-online.com/Ebo...throomgfci.htm