If I want to travel without check-in luggage, I pack a safety razor without blades (which I then buy at CVS for pennies). I have also traveled with my Feather Artist, with the blades in the check-in luggage. They made me open the carry-on, but upon seeing no blade, TSA was always satisfied.

As for a straight razor, sorry--too valuable and delicate to leave at the mercy of TSA. If I was away for enough time for it to matter, I would simply mail the razor to myself or a friend wherever I'm going.