Do you grow from seed or buy your transplants? If you use store bought transplants your choices will be very limited. So you'd have to focus on adjusting the growing conditions to eliminate all they contribute to thick skins. Do you grow in containers or in the ground? Do you want determinate or an indeterminate variety?

If you grow your own from seed then consider Sun Gold, Super Sweet, Coyote, Riesentraube, or Isis Candy to name just a few. But accept that with the thinner skins you will have much more fruit splitting.

Dave