Enchantments that change damage type

I was wondering for the skills that change your damage type (example Grenth's Fingers:All adjacent foes are struck for 20...68 cold damage. For 30 seconds, your attacks deal cold damage. When this Enchantment ends, all adjacent foes are Crippled for 4...9 seconds), will they activate those enchantmets that say while wielding a damage type spell (example Grenth's Grasp:For 20 seconds, if you are wielding a cold weapon, your attack Skills also Cripple that foe for 3...13 seconds)

To put it more simply will Grenth's Finger activate Grenth's Grasp even if the original weapon isnt a cold weapon. Or will Dust Cloak activate Ebon Dust Aura even without a earth weapon.

Thanks in advance.

Yes it does because if you use conjure flame while under kindle arrows, you will do extra damage.

It works in that fashion, however, to use two skills to activate what can be done with one skill and the proper weapon may be looked at as inefficeint. So, it would be better to have a specific weapon for that type of spell, but the answer to you quetion is very much "yes".