All cucumber peels are edible, and most of them contain plenty of extra fiber, Vitamins A, K, and potassium. Some cucumber varieties have thicker skins than others, so if the skin is too thick for you, go for a different variety. Be sure to wash the cucumber first, some cukes are coated with a waterproof wax that isn’t very palatable and can contain a lot of pesticides. Use a mixture of vinegar, water, and baking soda to remove the wax.