I know of nothing in the regulations, PTS, or Examiner's Handbook specifically requiring one to perform the calculations on a simple flight calculator as part of the XC planning task. As for use of computer flight planning programs (like DUATS or FltPlan.com) for that purpose, the PTS requires one to not only present, but explain the planning material. It's easy enough for the examiner to find out during the "explaining" part whether or not the applicant knows enough about the fundamentals to detect errors in the computer output due to operator error.
However, in addition to the preflight planning, the PTS also requires one to accurately compute heading, groundspeed, arrival time, and fuel consumption to the diversion airport while in flight, and that computer hooked to the internet back in the briefing room won't help you there, so proficiency with some sort of portable computation device is going to be necessary. That said, there's nothing in the books requiring one to use a manual device like a "whiz wheel" (E6-B, CR-2, or otherwise) versus an electronic calculator, although whatever it is, from a practical standpoint, it better be small enough to handle with one hand in the cockpit of whatever it is you're flying.