Weapons will always impact the DPS of any Melee class. Yes weapon speed affects attack speeds (haste).
I use a Naga mouse and I binded Cat Form on ''-'' and Bear Form on ''='' one next to another. Mentally super easy to know that the first one is my DPS form and second one is my living form. The way position my hand on my mouse makes it super confortable to use them for powershifting and fast effectiveness.
tl;dr
Haste is not the same as weapon speed. Cats have a base attack time of 1 attack/second which is affected by haste, but not the weapon speed itself.
Weapon damage is converted into feral attack power, which is what matters for you, so don't worry about the damage range on it, just the FAP value you get.