Back when the song was originally written, a crew member on a sailing vessel or ship was often referred to as a seaman. Sometimes, when a seaman returned from a trip, the seaman's head would show signs of sun burn and flakiness. So the captain would order the seaman to apply an ointment made of aloe and peppermint. This proved slippery but extremely moist and shiny. When the song was written, it was not uncommon to see shiny seaman all over town on the east coast, especially in areas of Boston and NYC. So the song refers to shiny seamen (shining "sea" short for seamen). Look it up.