Eric Dane isn’t a SWO. He just plays one on TV. But his late father, William Melvin, was an aviation boatswain’s mate in the Vietnam War era. To honor his service, Navy Secretary Ray Mabus presented Dane with a shadow box of his awards June 12 at the season 2 premiere “The Last Ship” in Washington, D.C., attended by sailors in the area. On the show, Dane plays Cmdr. Tom Chandler, skipper of the destroyer Nathan James and more or less humanity’s last hope of survival against an apocalyptic virus. “I’m here because I love Washington, I love the Navy and…