Killer whales eat sharks. Sharks have also been found in the stomachs of sperm whales. Most toothed whales, however, stay away from sharks because sharks eat dolphins when they can catch them. In the tropics, there is a shark that specializes on taking small bites out of the side of a dolphin. It is called a cookie cutter shark because it leaves wounds that look like they were made by a cookie cutter.
Dolphins have very sensitive skin.
A few years ago I went to help rescue a common dolphin that had stranded alive on a beach in California. We kept the animal wet and shaded until the veternarian arrived. Another time, I was at a mass stranding of sperm whales on a beach in Oregon and I walked up to a live 20 ton whale, an adult female lying on her side. I just barely touched her with my hand and she flinched. It is impossible to tell, of course, but I think the skin of whales and dolphins may be as sensitive as our own.