Necro skills healing zombies would be cool, and you should at least be able to poison body parts like other food items (some kind of "poison all foods in inventory" function would make this less tedious), but I think the main thing zombie chars need is more skills to remove and protect themselves from fire. I also think they should maybe only take 50% of the healing as damage (as in, a skill that heals for 50 will damage a zombie for 25). Maybe acid should also heal zombies? Probably not but worth considering.
Some kind of contaminate spell that turns fire to poison could be useful, perhaps a more targeted version that's more like magic poison dart that turns the surface the target is standing in into poison. Maybe a spell like bloodsucker for fire. I think the buffed decaying touch to turn healing from elemental resist above 100% will help zombies use poison to heal themselves and attack a poison healing target like skeletons at the same time.
Zombie has always been something you need to build a whole party around, so every class should have skills that synergize with it somehow.