As the others mentioned, you can exit any of the rides without riding.
However, your impression of which rides are "wildest" is a little bit off. Big Thunder Mountain Railroad is much "worse" than Expedition Everest or ToT. Expedition Everest is one of the smoothest roller coaters you can ride anywhere, and its biggest drop isn't as frightening as the big drop on Splash Mountain (despite being somewhat longer). In any case, Big Thunder will 'beat you up' more than EE, and in my experience, is more likely to induce motion sickness than EE.
ToT is one of those that's hard to convince people is pretty tame, due to the name and theming. But it really isn't the wild ride people think it is. It's the tamest of the freefall-style rides I've ever ridden, and most people I've spoken to about it agree that the actual ride is nowhere near as physically intense as they expected it to be.
Good luck, and have fun on your trip.
David