I'm not sure. The scabbards are 9 and someone is tending to them, Momo is just a boy, my Shinobu is pretty weak and Sanji doesn't know how strong this Yamato is. Moreover if the scabbard discovered he chose them over the shogun, they wouldn’t be that happy.
Not to mention Sanji meeting Yamato would probably solve both situations: Sanji can save Momo from King, have the obvious gag over Momo hiding in her clothes and then Yamato and Momo can go to the scabbards and help them.
Kinemon has to encounter Momo, he was kidnapped and he let him hanging there to attack Kaido.
Sanji going to the scabbards and dealing with Jack would seem a unnecessary delay, Yamato has to meet the scabbards and lead them. There will be no better opportunity. On top of that, if the tenth person is Hiyori, she might not only meet the second heir of the Kozukis but also take the Ame no Habakiri (i bet Hiyori brought that in Onigashima) from her.
Oden can't fight without Nitoryu, and Yamato has just a weapon