Haki is needed to defeat CC, not the slime. His gas logia can not be grasped without haki, otherwise rendering any physical attacks useless. Non-haki users could not touch him.
No real need to speculate how the slime will be defeated, Caesar already revealed it's weakness to the audience:
it's weak against water. Zoro, Sanji, and Brook will somehow figure that out and defeat the main body before it can finish crossing the lake.
I don't think that is what Law meant by "fast". The actual fight against the Yonkou will be slow and deliberate, he "didn't say that we could fell a Yonkou just like that...!! If we take things one step at a time and go with my strategy, [he's] saying that the chance might present itself...!! (
Ch. 668, P.2). When he said "fast", he meant that once the plan is executed events will transpire so quickly that "there will be no turning back", he was offering Luffy a "...last chance to back out" (url=http://www.batoto.net/read/_/103954/one-piece_ch668_by_mangarule/13]Ch. 668, P.13[/url]). He did not mean that they could sail directly from Punk Hazard to the Yonkou's headquarters. Big Mom has been shown to control multiple islands and have a large fleet. Chances are this will be a multi-island arc in the mold of Baroque Works or the Sabaody-Amazon Lilly-Impel Down-Marineford.
Law is a Shichibukai, a government official. He could have used his position to snoop around and find as much information about Punk Hazard as possible. Punk Hazard is not on the map, nor is it logged. He had to discover it by other means, he could have learned about CC and Joker while investigating records for the location of the island.
That does not mean he is controlled by CC. Clearly he is not. He has blithely been doing whatever he chooses: researching the notes left at the island, confronting marines, attacking CC's subordinates, attacking the Yeti Cool Brothers, and forming alliances with Luffy. Not once has Caesar given him orders or controlled him in any way. Funny how despite being "controlled" by Caesar, Law seems to be the one giving the orders when they
first met. Obviously there is no reason to believe Joker controls Law. It would be quite a stretch to assume that because Law knows of Joker, that Joker controls Law.