Link is canonically left-handed, but I guess we can accept that he's grown to be ambidextrous over the years. His Wind Waker in-game figurine also states not what his handedness is, but which hand he prefers to use. (It actually says: "Preferred hand: Left") That, and, well, considering how Skyward Sword Link is the first one ever to be truly right-handed...
Back when Zelda was young and didn't exactly know where its roots were, there were a lot of things going on and we can't really confirm anything for sure. The official art can be misleading. -_-;