I'll fix up Olivie.
Of the classes that we have. The ones that do not have AW skill outside of the black rarity are...
Ninja
Avenger
Mage
Witch
Shaman
Feng Shui User
As for Despara's AoE on AW Skill... I didn't notice that from the video nor is it noted in either of the wikis. She just has an incredibly fast attack speed.
It is basically a last resort skill. For a skill massive attack at his maximum. He hits everything within 360 range of himself for 2499 physical damage. This comes at the cost of around 3 seconds later taking 90% of his current health as damage.
Note that Rachel's range with skill active who can hit the entire map is 536.