I'll be honest, I've never subscribed to the Oden parallels with Zoro. To me they read as forced. I think the main connection between Zoro and Oden isn't that Zoro is suppose to be the "next Oden," living out his life, but rather that Zoro is picking up where Oden left off in finishing the job of beating Kaido. Oden was a powerful swordsman, so it will take a powerful swordsman to conclude what he started. In that sense, Oden is more of a benchmark Zoro will overcome, while bringing closure to Oden and his family's dilemmas. I think it contrasts well with Momonosuke, who must become a Shogun in his own right, and not one who just follows his father's footsteps. Back to Zoro, he's fighting for Wano as a samurai who lived out Oden's ideals for Wano. The country stagnated because of its xenophobic tendencies, something that wasn't always the case.
It's why I believe that Ryuma travelled the world in his youth as well, and that 'Monster' was a small window of his long journey back when Wano's borders were still opened. The three strongest swordsmen Wano has produced, (if we're to believe Zoro is of Wano descent), all travelled to become as strong as they were. In Zoro's case, strong as he will be. As Mihawk said-
And emphasized during Oden's flashback.
I interpret Zoro scarring Kaido rather than just reopening his wound as him distinguishing himself from the man who wielded Enma before, and that while he is fighting for Oden's cause, he has his own reasons for fighting as hard as he is. Namely for the innocents who can't fight for themselves, and those who died trying.
I also sorta hope that if he kills Kaido, it's through Santoryu, though I recognize using Ittoryu is also a possibility, especially since Oda has said Zoro's inspiration is Ryuma, and he's drawn many direct references to Monster. There's no way around that. Even so, I hope the people of Wano recognize Zoro as his own man, and a hero they were wrong about, and who inspires them to go out to sea and see the world.