Question: Is it permissible to peel a cucumber or carrot on Shabbat?

Answer: It is permissible to peel a cucumber or carrot on Shabbat, and there is no concern of borer involved. Since the peel is still attached to the vegetable, it is allowed even if you are not eating it immediately, as long as it is being prepared for use on Shabbat.

This is different from fruits like pomegranates or oranges, which must be peeled right before eating. Furthermore, it is halachically permissible to use a peeler as well.