The skin effect is actually the same reason why you're safer in a car during a lightning storm.

When the charge from the Van de Graff generator leaps to the cage shown in the picture, all the electrons stay on the outside surface of the cage, it is actually safe to touch the inside surface of the cage.

The electrons do this because they are like charges and repel away from eachother. They get as far away from possible from eachother. The surface of the cage satifies the electrons need to be as far away from all the rest of the electrons as possible.

However if you touch the outside of the cage while it's charged you're in for a big shock