This is a personal preference, but does depend somewhat on the type of cucumbers used. Regular cucumbers tend to have a thick waxed skin that is more bitter. It makes sense to remove at least half of the peel in this case. English and Persian cucumbers have a thinner, milder tasting peel. Many people completely skip removing the skin with these easy-eating cukes.  Keep in mind that most of the vitamin K in cucumbers is in the skin. Plus it has fiber and antioxidants, so you’ll get more nutrients from the veggie by leaving at least part of the skin.