It may be because I have the Warbringer talent, but unlike most class abilities, I found out I can use Charge as a Zombie last night (an entirely accidental discovery).
This seems buggy, but is quite fun. It helped me stay up a few minutes longer against an Undead Mage who decided I'd had enough fun taking out guards and quest givers outside of Splintertree Post. Tested a few other abilities and that was the only one I found that I could still use as a Zombie.
Has anyone else found class abilities that are usable as a Zombie?