It was done. There was a time when razors were not considered weapons just yet, they were small and easily conceilable. And I guess it was a fad weapon just like th ebalisong which is meant primarily to look cool, but otherwise sucks as a knife.

Razors actually make lousy weapon for an actual fight. They easily break or chip, it might close on your own fingers, has no decent handle, etc. The one thing they're good for is quickly cutting up someone really bad if they can't fight back or are at least not armed themselves.