This Zunesha info is what Momo got from his conversation with him. He was the one informing Yamato and not the other way around.
A big thing people are forgetting is that Oden is aware of how dangerous the info he got from Laugh Tale is yet he voluntarily left the journal for his family. He didn't even tell his scabbards anything important from his adventure out of protection for them. Why would he leave information blatantly about what the one piece is and void century stuff to make his family a target?
Yamato is most likely going to leave him again. Momo still has to pull away Onigashima and Yamato knows she isn't of help being with him. She's ditched him twice to help the alliance so it's not a shock that she'll do it again.