What kinds of swords did the British Royal Navy use in the late 1600s to the early 1700s?

I want to know what kind of swords the British Naval soldiers were using during the golden age of piracy. I know Blackbeard's crew were killed off by rapiers while they themselves used cutlasses. But apparently Maynard's rapier plan was very risky, which leads me to believe that rapiers were not the standard sword of the royal navy. Please cite sources!