I think I figured it out. King is basically like kaido. Kaido took multiple stab wounds and even an attack on his internal organs(gamma knife) and still barely looked injured afterwards. Why? Because Kaido's mythical zoan has enhanced healing properties. King is just like this but due to his race combined with his zoan, his regeneration is far stronger, possibly even close to marco's level.
The way you do lasting damage to kaido is to use ACoC, as was done by Luffy, Zoro, and Oden. By hitting kaido with CoC, for whatever reason, it makes it harder for him to recover from the damage.
So, in order to defeat King, Zoro needs to hit him with an ACoC infused slash. At the moment, enma is going berserk. Right before Zoro scarred kaido, we saw a panel of enma with a white aura surrounding it. Given how Enma can draw out CoA, it is also possible that enma can draw out CoC in a user. Zoro will master enma and use it to draw out his CoC, allowing Zoro to hit King with an ACoC clash and deal damage to him that he cannot recover from.