Can you ask to be anesthetized?

If you’re getting surgery done on a certain part of your body (doesn’t matter where) that isn’t super major and instead of putting you to sleep they just numb the area that is required (say foot or hand) and you can still be awake you just won’t feel them doing surgery. Can you ask them to put you to sleep? Cause I’d probably have a panic attack while their doing surgery on whatever part if I was still awake while they’re doing it.