Can class-skills that are properties of certain weapons activate on all classes?

I obtained a unique sword that haves 10% chance to cast Eviscerate. Since Eviscerate is Berzerker class skill, could other classes cast it if they used this weapon?

This is certainly possible.

I have a 15% chance to cast Blinding Cloud on my righthand weapon. As an Outlander, I do not have that skill (I'm not sure as to what other class it belongs to).

Here you can see me casting it on the dummy (I was only doing regular attacks so it's most definitely the skill):

According to a runic forum thread, the weapon proc "Eviscerate" is not the same as the Berserker Eviscerate skill, even though they share the same name. In fact the weapon proc seems to be weaker than the Berserker's level 1, and any class can use it.

Weapon proc Eviscerate: 70% weapon DPS, no bleed

Berserker Eviscerate level 1: 88% weapon DPS, bleed for 6 seconds