Bear in mind that the plural of anecdote is NOT data.

However.

For the last year I've been shaving with about 60 different razors, all but four of which have come from eBay. I've cut myself with badly rusted blades.

No illnesses.

The odds for catching something from a razor are quite low. The most effective preventative for surface-transmissible diseases is washing, which razors get rather more thoroughly in the course of their regular use than most other items.

Any virus, bacteria, fungal spore or prion which survives sanding, polishing and honing deserves the chance to get higher up the food chain.