You don't want to peel them. They won't have the right texture, I don't think. But you can't use waxed ones, either. For good results, you need to use cukes that are either A. specific for pickles, or B. immature table cucumbers. So if you are buying them, rather than growing them, you'll want to buy pickling cukes, and they are not waxed because they are specifically for pickling.
Another option, the organic Persian cukes that Trader Joe's sells might work. I haven't tried them for this purpose, but they are immature, unwaxed cucumbers.
Cukes that are good for pickling have a more tender skin than most table cukes, that's a part of how you get the texture. If you use a mature table cuke, I think it will turn out with really tough skin and just mush on the inside.
Because it's hard to source pickling-grade cukes all year, cuke-pickle-making is usually a summer thing. However, there are lots of other great fermentables right now, like radishes, cabbage, just about any Asian veggie, turnips, carrots... the list is long.
Hope that helps! The book
Wild Fermentation is at a lot of libraries - I think you'd really benefit. There is a lot of free info on the website, too.
Sandor Katz's website Wild Fermentation