You can hurt Kaido without conq haki, if you have really amazing ap or advanced armament haki. It's just another upgrade and boost to ap.

Moria did fight Kaido, but we don't know how well. At the end, he lost everything he had after the fight. You can say similarly Don Krieg fought Mihawk for example.

By the way, Moria could possibly have conquerors haki in the past, as he had a big dream. But he lost it since, and that led him to the warlord position.

Technically, someone can fight Kaidou without Conqueror’s Spirit Haki, they just might not win unless they have advanced Armament Haki or some Devil Fruit power that can bypass his natural defense. Moria lost everything except for his life when he fought Kaidou in Wano. Now that I think about it, I wonder how he escaped….

Moria might have had really good haki at somepoint.

Yeah he had onion haki

I mean… we know Kaido beat him and killed his entire crew.

I wouldn’t call that much of a fight

This fighr happened after Oden, Kaido still remembers Oden as his greatest rival and doesnt even remember Moria so... not really a fair fight it was more of a massacre