i have a feeling if somehow Yamato will be spotted by the Marys, and King will go for her.
And then Sanji will intercept.
As for now, i think Kinemon is going to be the one meeting Yamato. Sanji has to know Momo is not safe before acting so Bao Huang has to notice Kinemon and the puppet before communicating to King that Momo is alone with Shinobu. Only then, after Marco gets defeated and Momo has no real defence, King will try to kill him and Sanji will save him.
If Oda wants to keep it simpler, King might just fly directly to Kinemon and Yamato's floor in front of Sanji, forcing Sanji to block/attack him and only then everybody discovers that that Momo is a puppet. Sanji doesn't know how strong Yamato is but he knows Kinemon would be no match for King.
The real Momo would be safe.