Electric shavers are allowed on board. In fact, the operation of them on board is specifically allowed by FAA regulation, along with pacemakers and hearing aids. So, it will be no problem to take your electric shaver on board in a carry-on. I have never had any problem aside from a couple years ago when they opened the case to verify what type of "electronic" device I had in my bag.

Now, shaving cream or other grooming liquids, gels, and foams in quantities more than 3 ounces may be problematic in carry-on bags.