If Leia is Stunned, would she still be able to use Battlefield Leadership, forgoing the attack portion of the ability to command another friendly figure to attack a target?

I would lean towards No

Battlefield Leadership is "Do X, then Y"

If you can't do X (Perform an attack) then there's no Y

I think it would be different if the orders were swapped though

Yes, she can use Battleship Leadership to waste an action. When resolving Battleship Leadership she cannot declare an attack while stunned, declaring an attack equals declaring a target, thus because there is no attack there is no target,the other friendly figure doesn't have a target for its attack, and thus the attack cannot be performed.