Actually Legacy Weapon is fairly useless against U/W control.
#1) Your Idea only works if legacy weapon is on top. So until it is you will still lose two cards a turn to the millstone, plus you draw a card.
#2) If it is on top of your library you still lose one card to the millstone and draw a card.
#3) If Legacy weapon is drawn then you must have 8 cards to discard it, and if you play it they will just let it sit there.
#4) When Legacy Weapon is the last card in your library any intelligent U/W player will just let you draw the weapon.
#5) Most millstone decks use Howling mine as well.
#6) Most Millstone decks use more than one Millstone.
 
Therefore, You could never deck a U/W millstone deck with this strategy, because you are still losing more cards than them every turn, and you will eventually be forced to draw a card that isn't there.
 
Still, if you had a deck that was based around legacy weapon it could certainly help, and could destroy howling mine as well.
Also, your Idea CAN work IF the mines are not present.
 
Thanks for reading this far,
Donald Shults