So, my only other friend that has read the Cosmere books developed a theory about ChayShan, and with his permission, I will post it here with some additions made by me to his theory.
This is going to use the idea that if two Shards cooperate on a planet to make humans or allow humans to gain sentience, there is the first Shard's magic system, the second Shard's magic system, and the magic system that came from their cooperation. We can easily see this on Scadrial, with Allomancy as Preservation's, Hemalurgy for Ruin, and Feruchemy as the balance. It might not follow this pattern, and I will address this at the bottom of my theory. For this I will take ChayShan as the balance magic.
So we know that ChayShan is like Tai Chi, a group of stances similar to a dance meant to help to your body. Shuden performed it when Sarene was teaching the women how to fence.
Feruchemy required a user to be weak or disabled for a time in order to draw it out later. ChayShan might be slightly similar to Feruchemy by the power from self aspect. It could be that ChayShan taps into both Dominion and Devotion then uses them to achieve better balance, speed, endurance and strength to access later on.
Then, after the battle, we get this from Raoden.
So my theory is that ChayShan is tapping into the Dor and the Skaze through some weird balance that is created by the dance.
And now if ChayShan is not the balance magic. Brandon Sanderson said that Skai gets the Skaze, not a magic system, and they are like evil Seons. Because Skai doesn’t get a magic system, there really couldn’t be a balance magic.
If Raoden was correct about this, then ChayShan might just be drawing a type of Aon in the air while dancing, that can then be accessed later for the power. This would make more sense because if ChayShan was the balance magic, Dakhor would be the other magic system and it seems to function on the same principles of AonDor.
Well, this is my longest post yet, but I think I will be posting one close to this length on the Nahel Bond soon. Hope everyone likes this theory.