As a child growing up in the 1950s, Dean Potter spent a great deal of time outdoors working on his family’s Rhode Island farm, playing at the beach and sailing on the bay. But he didn’t use sunscreen, because the product was still in its infancy back then.

“In those days, you put baby oil on to get the first good burn of the season, and then tanned the rest of the summer,” Dean says. “We didn’t know any better.”

So, when...