As is often the case with this set, the rough thing about Lost Souls is that it blocks all the good options you could have. Going from Vitality to Chaos, if you were to go Cabalist, you’d go from a double RR class to a 0 RR class, and you don’t have double trees + cat to give huge flat damage to make up for that, compared to going Chaos Conjurer. No weapon to provide Chaos RR, no Conduit for either Occultist or Necro to give good RR either. You’re stuck with less than ideal equipment and the set doesn’t do too much other than beef up the Skeletons and give a second Hellhound.
If you were to go Skeletons alone, however, you have a few decent options - either Inquisitor or Demo. Demo has more RR in Thermite Mines, while Inquisitor has the heal and Vigor for more Skeleton Health. It’ll likely go Apostate, in which case I’d like to know how Chaos Skeletons compares to my above Fire Skeletons.
If it weren’t for Reaper of the Lost being the most difficult Nemesis, I’d have a hankering to try Aether + Chaos Skeletons just take advantage of all those skill points in the Voidwhisper Rings + flat damage from Bysmiels Domination. I’ll leave this link here in case I ever want to revisit whether to switch it to full Aether pets or Chaos pets: https://www.grimtools.com/calc/eZPjK3B2