Well realistically speaking, Zoro is the only one in the crew who can kill Kaido after he's defeated. When has Luffy ever killed anyone deliberately?
Having said that, I've always had a gut feeling that Kaido won't die this arc. One, because Luffy has never killed anyone. Two, because Oda himself has said that he doesn't make Luffy kill the villains he's defeated because Oda believes that living in defeat is a worse punishment than death. Ironically, this would also especially fit Kaido since he has been trying to kill himself (truthfully or not), and also believes that it is only in death do humans reach true perfection (said during his fight vs the Scarabs on the rooftop). Kaido living in defeat as a loser and not dying in battle would be a much crueler punishment for him.
In addition to Yamato's latest comments to Kaido about kicking him out of Wano (not killing him), plus Kaido's alliance with Big Mom wanting to take over the world together means that Kaido hypothetically speaking will have to physically leave Wano himself someday anyway, which is also why he wants Yamato to be the new Shogun and rule and guard over Wano in his absence, which i don't see happening-because that would mean that Kaido got what he wanted from Yamato, which runs counter to what Oda has done this entire series, destroying villain's and their dreams by defeating them in battle so they can never achieve their objectives.
Other than kicking Kaido out of Wano, i think the other big objective that victory in this war is supposed to achieve is defeating and destroying the Beast Pirates so they can never be a crew again, or as strong as they used to be. This would make it hard, if not almost impossible for Kaido to control Wano again.
The issue isn't whether or not Zoro will or can kill Kaido, the issue is will Oda allow it to happen.