There are a number of chemicals under various names that "reverse" the rusting process, or at least take off the existing rust. The problem is that you are left with pits and surface irregularity where the rust once was. so you'll probably want to sand it smooth anyway.
Electrolysis works the same way, and probably cheaper since your using household items. Basically electrolysis is a "method of separating chemically bonded elements and compounds by passing an electric current through them".
And in our case it would mean removing rust from steel by emersing the razor in a solution of water and baking soda then applying an electric current to the bath of solution. I've never used it on a razor, but have done car parts with a 20 gallon barrel set up. Really, very simple.
http://www.ighunters.net/metal/electrolysis/equip.htm
This website is a good simple electrolysis set up, but you can make as big a tank as you want if you have enough power, like a car battery charger, etc.