I dont think Law will, because he is more of a "hax fighter". He is also not know for having CoC at all.
Kid on the other hand was even highlighted by Kaido as CoC-User. And there is a reason why Oda havent shown CoO, CoA and CoC with Kid, even tho he already told us Kid has all 3 of them. Additionaly, when Law asked Kid if he has still something up his sleeve, Kid refused to answer.
I see a high chance for Kid using aCoC against Big Mum, at least for the final blow.