He is left handed because Miyamoto is, and thats why in the master quest for GC and 3DS he has it in his right hand, as it is reversed. Only the wii ones are right handed because most people are right handed
I don't think it's fair to say that Link is really ambidextrous. To state the obvious, everyone seems to forget that Link is different person in nearly every game, so you can only assign a hand of dominance for each separate Link. That being said, I don't think any Link was truly completely ambidextrous. He does need to wield the shield, but there's a reason it's held in his non-dominant hand.
I'm pretty sure every Link is left handed in the canon of the game. Why is this? Skyward Sword and Twilight Princess both had their gameplay switched to right hand for the simple fact that the majority of people in the world are right handed. So accordingly, everything was flipped to adjust to that (I'm not sure how a righty would fight a lefty in a sword fight as I've never seen one myself).
IRL: Link is a righty in SS/TP/OoTMQ (and OoT3D commercial I think -- when pulling dat a...Master Sword, he held it in his right hand in triumph although in OoT[3D], he holds it with his left).
In Game Canon: Link is a lefty in all Zeldas.
Of course, Miyamoto I'm pretty sure gets the last word on these matters, but I'll consider Link to be a lefty, as his old title of "Left Handed Hero" expounded upon until Miyamoto/Aonuma gives any official word.