Can I carry a disposable razor in a carry-on bag?

No, just buy one when you get over there and toss it out when you fly back. You can buy one for less than a dollar. Have fun.

Yes, disposable safety razors are specifically allowed. See site below and read under," Items permitted in aircraft cabins."

Best to have shave before you board the flight,then keeping them in your checked baggage. This way you won't end up shaving in jail!