Once upon a time, in a simpler age when electricity was expensive or balky, windup razors were popular in Europe and Russia.
In the Space Age, you could even buy the NASA-approved version!
But except for vintage models (a mere $100.00), purely mechanical razors seem to have vanished from the marketplace. Although in this era of environmentalism, it seems they should fulfill a certain demand.
The closest such product I can find cheats by using electricity--though it is hand-cranked!