Is it permitted to peel a cucumber and a carrot with a peeler on Shabbat?

Shalom rav, 

Since the peel of a cucumber is fit for eating, and most people eat it, it is permitted to peel it on Shabbat, even with a peeler. And even if one does so for the sake of another meal, it is permitted (see Shmirat Shabbat Kehilchatah, part 1, chapter 3, section 34, and Chazon Ovadiah, Shabbat, part 4, pages 231-232). However, the peel of a carrot, which most people do not eat, may be removed only with a knife that is not specifically made for peeling, and one must also be careful to do so only close to the meal (see Shmirat Shabbat Kehilchatah there, section 35). 

With blessings, Hillel Meirs