Easy solution:
Just test it. Change the weapon and see if the skill is still available. Some skills are more specific as others. If I remember correctly Whirlwind works fine with staff to deal magic damage instead physical. Not sure about two handed, some could use only the main hand. Just change the weapons and compare the damage. Surely easier than asking here, don't thing anyone knows every little possibility. Not every weapon dependent skill adds in also the elemental damage, I think.
Daggers are for sure the worst kind of weapon for Warfare skills like Whirlwind, their damage is really low and depends on backstabbing.
