I know exactly what your talking about. When I bought my first jar of Proraso, I thought, This does smell familiar, It took me a while to remember that it was Noxema.
Menthol aside, they are very, very familiar in composition too.
I've never done a side by side, or compared. Noxema is a facial cleanser, I can't see why it couldn't be used, it cleans and opens your pores. Some guys use straight olive oil. Why not test it and post your results....?