I don't remember what I ate last night
but I can spout off obscure rules to all sorts of game like nobody's business!
That's not how it works. You can only take advantage of one set of equipment per turn. If you rolled the one-handed weapon, then one of your hands is still using that weapon. You can't switch it out.
What's the point of Magic Hand if it doesn't allow you to add extra equipped items to your fight? If you start with one hand free, and use Magic Hand to add another free hand, it seems possible you could add a 2-H weapon with your two free hands.