You say you're on a "desert island" and can't get hold of a brush or shaving cream, but you do have access to internet and a computer?

I'm not trying to insult you in any way, I just find it a bit amusing

In theory you can maybe find several different stones that can help you make the razor shave, but if you have a postal service why not send it to someone for honing, and maybe they can throw in some cream or soap and a brush in the package when they return it to you?