On my current play through I am doing a pure mage character who never uses weapons of any kind. I made it all the way through the CoW quest line and Dragon Rising with my favorite weapon listed as "None" But that was all ruined when I did the Final Descent quest since you have to swing that blade at the wall to get out of the dungeon. Not only do I now have a favorite weapon, my Two Handed skill actually incremented a little bit!

What's a mage to do!

Well you could say that that`s the only weapon you`ve ever used so you may prefer if you were forced to use a weapon

And that one swing gave some experience with handling a two handed weapon
No a lot, but some
Maybe just enough to hold it properly