No
You are considered to be attacking with your second hand on the weapon.
You are holding the weapon in your other hand, thus it violates the "with anything in it" clause.
No
A shield requires an arm, not just a hand, to wield:
Anyone can…strap a shield to an arm.
PH, Armor and Shields, p. 144
This jibes with real-world use of the large shields, where the arm provides necessary support to make the shield useful. (Bucklers, or hand shields, may be a different issue, but there are no bucklers in official D&D 5e rules.)
“Manipulating an object” (Mage Hand, PH. p. 256) is different than wielding it.
Mage hand is not strong enough
The hand can only carry 10 pounds. A melee attack can involve thousands of pounds of force — orders of magnitude more than enough to overwhelm the carrying capacity of the hand. Even arrows project much more force than 10 pounds. (And since the hand is not connected to the ground, this force could bat the shield away like a piñata.)
This jibes with the spell description that says Mage Hand “can’t attack.”
If it can’t “wield” a shield, how about just holding it?
Just holding a shield up might convey some benefits to anyone behind it. Depending on the situation, the DM could rule that it provides concealment from view, or some other benefit.
But that’s not wielding a shield.
Best Answer
RAW, Your hand is occupied.
The description of a Shield in the PHB states...
Emphasis Mine from PHB p144
Thus, the PHB seems to be referring to shields that are 'held' with the hand, not simply 'strapped' to the arm.
In the medieval era, this was the norm. You'd either have a handle you gripped, a handle + a strap, or two straps (but you'd hold one of them in your fist). If you just strap a shield to your arm and don't have it mechanically affixed to your armor or something...the first time something hits it, it's just going to spin, hit you in the face or legs, and then be useless...because there's nothing holding it in place.
So, the back of your shield probably looks like this
or like this