Consider me team squirrel...though I also love the idea of having the faces be different animals/figures of chaos (from various mythologies), in which case the Lord might be an overcoat with all the critters inside (and whichever face you roll is the head you can see leading the rest for a bit)
I'm not really a fan of having a child as the Lord...I don't think children are truly chaotic (they are just very impulse driven...but their impulses have logic based on what stimuli the child has been exposed to).
From the original Fates dice, I enjoyed most of the faces, though I found Clockwise a bit tedious (too much moving stuff), and the 14 point star was really unusable to me (okay it was usable, but I never remember what each die causes it to do, so it's constantly looking up what I have to do for it, which is tedious) Both of these I just feel were almost too many moving parts...too much to remember/do.
I think it might be fun to have a topsy-turvey face, where you have to flip another die/dice (so literally turn a die so it's top facing face is now on the bottom and what was on the bottom is revealed) Or a tilt face, where you turn the top of a die so that side is now facing towards the Chaos die (like it was tipped towards the Chaos).
It might be neat to have a "this is not the right tool for the job" face, where you pack up your dice and pick another divining method to use to get your answers. Or alternatively an "I need more input" face, where you leave the dice as they are but grab another diviniation tool to layer with the dice (draw a card, use a pendulum, cast some charms...whatever floats your boat).
To take a note from dexterity games, you could have a face where you have to flick the Chaos die at another die (the nearest, the farthest, the one that would put the most dice inbetween)
If you want to get really crazy, you could have a face that tells you to grab the reading cloth by the corners, give it a shake, then plonk it back on the table (though that would require that everyone using the die had a cloth...so maybe not lol)