In "Zuko alone" episode, Zuko is carrying his swords on his right hip, meaning he will draw them out with his left hand, which means his left hand is the dominant one. Zuko is canonically left-handed.
Being left-handed myself, I’d be delighted for a canonically left-handed Zuko.
As for drawing his sword, he’s pretty consistently shown to be drawing it with his right hand actually:
With this one notable exception (when he has fire in his right hand):
Considering he wields dual swords, he probably would have trained to be able to do everything equally well with either hand.
But there are other things supporting that he may be a left-handed person who was forced to use his right hand for traditional reasons from young childhood, or that he is truly ambidextrous.
He plays with his dagger with his right hand, but uses his left to cut his hair.
He catches and instinctively reaches out with his left hand a lot:
He uses his right hand for writing, but left hand for drinking, pointing or reaching for something:
