Heh well obviously you wouldn't be using a 6Ist weapon with WW, the point of Berserk is you only need one weapon for killing. For WW, the only reasonable choice is dual Grief, it's miles ahead of Oath/Death/botd and then lightyears ahead of everything else. Edit: More like lightyears ahead of everything to be honest.
CBF isn't as important for a WWer as a Berserker, possibly to the point where it's not worth getting if you control your whirls well. With Berserk, it slows down your attacks and your horking, with WW it only slows down your horking, ideally. Based on the limited WW Pitbarbing I did, it was still worth having, because in practice you whirl less than perfectly, and when those whirls are slow you lose a lot of time. You also do some limited amount of running all the time, which would be super annoying to be frozen during, too. That said, it's probably worth trying without and see how you like it.