Cleaning your razor woudl be a good thing, and depending on your own preferences you can go up to disinfecting it even. Rinse with hot water and maybe some soap, if you want use disinfecting soaps, or use some rubbing alcohol. If you have some alcohol-based AS or and EDT/EDC lying around that you don't like, that contains a fair dose of the good ol' germkiller as well.

When I got my razors in, I just used some hot water and a bit of soap, but it's part of a personal preference of course and how reliable you view your sources.