The shield is giving you defense bonuses if you're holding it and have proficiency. Weapons don't normally give static bonuses like that, but I see what you're getting at.
What do you mean "incapable of using it to attack"? The rules on magic weapons (PH 232) say that if you're not proficient with a weapon you can still attack with it, you just don't get a proficiency bonus. The rules for magic item categories (PH 231) and properties of magic items (PH 225) don't seem to put any restrictions on how the wielder benefits from those. It seems like you'd just have to be holding the weapon.
4E doesn't seem to define handedness, other than the other hand from the one you're holding an Off-Hand Weapon in. The rules on 215, 217, and 270 say you can attack with a single weapon using either hand, and don't define any penalty for doing so.
So if you have, say, a longsword in your right hand and dagger in your left, and drop the longsword, there's no need or requirement to switch hands in order to attack normally with the dagger.