Buy some scrubbing bubbles and a toothbrush with medium soft bristles.
Spray the razor with scrubbing bubbles and let it sit on there for about 5-10 minutes, then scrub with the toothbrush. Rinse off. Repeat if necessary.
When it's as clean as you would like it to be, wipe it down with some rubbing alcohol and let it dry. Should be good to go.
If you really want it to shine, you could polish it gently with a microfiber cloth and some Maas metal polish.
Randall. BOTOC, Excalibur, Hot Sauce Pepper Heads Club