@The:
I think there's a good chance the Yonko Law wants to bring down is Kaido. I mean…it gives Oda a chance to officially reveal, in some detail, the final Yonko.
Luffy and crew could know who each and every Yonko is--each and every strongest player is--before truly setting foot in the New World; Punk Hazard is just the beginning. Once the Yonko Law wants to go after is officially revealed by name, during a conversation I'm sure (between the Strawhat's and Law, maybe CC and Monet in there too), we can find out info about Kaido; like beli bounty, strength of his forces, backstory, his Devil Fruit and Haki abilities etc--the same discussions can apply to Big Mam as well.
Also, and this is just a feeling (and theory), I think Kaido will be the science and technology Yonko (i.e. a cyborg crew member, a giant metal moving town/city...thing etc). What better place to officially introduce him then during a story arc that has a lot of science going on and a technology-feel? (Also, we were introduced to Blackbeard being a Yonko during Fishman Island, Big Mam being revealed during Fishman Island, and Shanks being revealed to be a Yonko even earlier in the series; why not 'Kaido time' for Punk Hazard)?
Maybe CC is doing work for Kaido; a scientist of the Kaido Pirates.
I like it. Personally though I don't want Kaidou to be a DF user though. Take Krieg + Million Times Stronger + Actual Story and Background + Intelligent enough To Have a Good Reason to have Scientists Under Him = Kaidou
Kaidou was mentioned as being strong enough to wipe out all of Moria's crew (before Moria became lazy), so I would like to see a brutal person who would do anything to defeat someone (Krieg again).
Sadly, Big Mom still seems to be the most likely Yonkou.