I use hot water to clean my carbon blade off, and then do the final dry with one of those Kleenexs that are infused with oil.

Seems to be a simple and effective method. I have a small disadvatange because I might shave with the same balde tomorrow or next year, never really sure. I just started rotating between two, a carbon and a SS. With the stainless I just dry it off with a towel.