USMC Harriers regularly take-off from the flight decks of US Navy ships without the aid of either a catapult or a ski-jump. However, rather than a large aircraft carrier, they are taken to sea aboard Wasp or Tarawa class amphibious assault ships, which are quite a bit bigger than the British carriers:
The US Navy -- Fact File
If it was necessary to operate Harriers from a large CVN, I guess that the normal landing area would be used for an unassisted short take-off run. Alternatively, launches could be made over the bow - but I would suspect that a centreline and some distance markers would be painted onto the deck to aid the take-off run.
I did hear that as there is a limiting speed at which the nosewheel can hit the ski-ramp, the latest generation of Harriers, with more powerful engines and a better wing, would be better off without it.