I dont see why it wouldn't work, as long as Sir Nick is booked and one of the DPS takes the stun.

https://deadwoodjedi.com/speed-tunes/slow-hellcat-unkillable/ 

This is a *relatively* low speed team that can do an easy 2-key UNM. You can substitute Santa for Helicath without having to change anything else.

You can't extend UK so eventually the stun will kill you.

Derp, right, I overlooked that.

Still, the slow hellcat comp will work with Santa. You stun target has to be tanky enough to survive the hit, but that shouldn't be too hard with Santa's shield and continual heal.

If you don't have doompriest, Odachi is a rare who can put up the block debuffs, he's also surprisingingly tanky and brings his own shield + def buff. I used to use him in my first UNM comp.

It's more a problem of trying to control the stun target while everyone has fluctuating HP.

So you don't want Valeries but the good news is he's easier to use than Maneater. Maneater does 2 turn unkillable on 5 turn cd. Nic's is 4 turn which means that Painkeeper might not be needed. However, Nic does NOT have the Block Debuffs and you need Block Debuffs (usually)

It will take some trial and error but here's how it works for CB:

Your stun target goes really slow, so that in the 2 turns for the buff duration the Demon Lord takes 3 turns. 2 of those turns are AOE that everyone needs Unkillable for and then only the 3rd turn does single target and thats where Stun Target comes into play being slower.

As for controlling Stun Target, I think it is actually easier to do Stun Target with Unkillable vs. Block Damage since Stun Target is largely (but not purely) based on THEIR hp% compared to everyone else. 

I recommend posting your roster so we can see what you're working with. The fact you don't need to waste 2 slots on champs like Valerie is actually great news for your damage. What you will need is a Block Debuffs and to make Stun Target easier, someone who does team heal HP based on the caster's HP and not the targets. Nic's Continuous Heal might make the stun target situation easier, since the stun target will be taking less turns and therefor not get the healing as frequently. MIGHT.