It's not that hard to see you could use your right hand to swing the sword even though Link is left-handed...
Flick your wrist to the right and Link swings (yes, with his left hand) horizontally to the right. Vice versa for a left swing.
However, I'd much rather be pressing a button in combination with the analogue as we've been doing with the previous Zelda's, it'd just get annoying after a the novelty has worn off.
I think the controller being used as a sword/bat/weapon etc suits party games a little more, where you're friends are round and you're getting drunk and swinging it around for a laugh... on my own i'd much rather sit still and press buttons as opposed to flicking my wrist here and there.
Although bring on the FPS games!!!! Woo!!! Ha ha.