Zoro will gave up something extremely important to him and that has play crucial role in his strength just because a Woman who he met few chaps ago ask him to?? Don't make me laugh.
Especially if Hiyori doesn't specifically say " the only sword that wound Kaido"....... literally Zoro won't just let it go.
The fox dude tells him everything about Shusui and Wano, Zoro doesn't give shit, only what he say is that's my sword blah blah lol. Still same Zoro right!! Why will he soften his heart just because some ppl who he met recently ask him.
You said Zoro already gave up Shusui before he don't know anything about Enma. Lol it was when the name Enma is spoken to him for the first time that make him gave up. The final conclusion is when Zoro said "No i will keep this with me, if i can master, it will make me even "stronger".