I've just noticed theres no unsheathe animation when you use your weapon in your LH. In the RH it unsheathed normally.

So if you want to save a second or two, use your weapon in your LH.

But one thing, you can't poison your weapon if its in your left hand.

Can you carry a shield in your right hand if you have a weapon in the left?

yes

and also kind related. when you are over encumbered you can walk faster in 3rd person

I'm pretty sure shields are left-handed only.

In the settings you can say if you're a lefty or righty (on xbox anyway) though I don't know what that does to the game, it would stand to reason that the sword would move to the left and the shield to the right.