The original point being that even if you switch your attack somehow you are still doing lethal damage. If a Great Axe does 2d6 damage with a full swing using its' blade, there is no scenario where you could use that weapon and do 2d6 damage without it being just as lethal.
The only way I see you being able to subdue someone into unconsciousness without it being potentially lethal is by using some form of grapple to put them in a chokehold or by concussive blows to the head. These forms of attacks would obviously not do as much damage as attacking someone with the full force of a weapon designed to do lethal damage.
