I would say ambidextrous. But for the most part he is left handed. The only reason they made him right handed in Skyward Sword was because it make it so the people who played it (mostly right handed) would be able to play it with ease.
Like others have said, I feel that it just depends on the game. I suppose I could see him as ambidextrous, though. Yet while he certainly is left-handed in many more games than he is right-handed, I can't see him as being either really, on a whole. I think he's whatever the player wants him to be since it varies from game to game, and ultimately, I think it's an issue that doesn't matter very much in the grand scheme of things. :>
Realized this not long ago but I was thinking of this thread at the time. With me I can use a sword in both hands but my left is best and if I use one sword I usually pick my left. I bat left handed also. Yet at the same time there are things I do right handed. So I think Link is a lefty but if he uses things in his right hand it might be because it's comfortable to do that for him.