Kan Ki already knew he was in shit when Sei arrived with an army, so no need for pretenses.
That said, it's my headcanon Sei has already let Shin know he will make Kan Ki an example of the Power of Law once he outlives his usefulness, and that he'll leave the task of capturing or eliminating Kan Ki to his entrusted sword.
That would make for a nice flashback: a conversation between Shin and Sei in the bloody aftermath of Eikyuu. It would also explain why Shin has managed to keep relatively calm and civilised around Kan Ki.
It's been my wishful thinking that we'll see that flashback at some point when Kan Ki flees a battlefield and considers which state to defect to since his army has been wiped out and he made an enemy of the king, only to be confronted by Shin and his retinue - including Na Ki for dramatical purposes.
I want to see Ei Sei exhibit that kind of forethought and confidence in Shin's abilities to handle it, but more importantly, I want Hara to make it clear that Sei considers Shin a failsafe within the Six Great Generals because he will never betray him, and I want to see Sei specifically thinking of Shin's slaying of Hou Ken and greatest feats as the source of his confidence in his ability to keep the Second Generation of the Six Greats from turning against him.
When Kan Ki meets his demise, I want to Hara either skip to off panel the battle entirely, or give us a proper sword duel between Shin and Kan Ki, resulting in his smiling death. I also want to see Na Ki straight up kill Rin Gyoku, or spare his life and allow him to join the HSA under his protection as a member of the Na Ki clan. Kyou Kai shouldn't even bother with Koku'ou. I imagined she'd be subdued quite easily and arrested, alongside Ma Ron and whoever else survives and/or surrenders.