I guess I should have clarified a little.
If a weapon is too slow, then donāt use it. This varies with your skill and strength, so for example, that axe, for you, sucks ass, but if you were stronger and more skilled, it would be good.
This is because if you are too slow, zombies have an easier time catching up to you and cornering you when in groups, and even if you kill with every swing, those groups will be able to get several hits in while you do. It also makes fumbles and misses very painful.
Notice the emphasis on too. Once a weapon is under āacceptableā swing speed, even if itās a little slow, I start looking at other qualities. That Zweihander is not something Iād wield at low skill/strength, but once skilled enough, Iād probably grab it unless Iām primarily a ranged character (too big to be wielded fast for a backup weapon), or Iām running with eskrima or niten.
Another similar caveat is if itās too weak damage-wise, like for example most knives, Iād probably pass it even if they play nice with points 1 & 2 and Iām looking for just a backup weapon. Even high swing speed canāt make up for not being able to kill the enemies fast enough, not being able to punch through armor is also a concern, unless youāre carrying a backup (or primary) weapon to do just that.