It would all probably depend on knowledge from Zabuza's side. If he knew beforehand about Hidan's abilities, he would probably use his Silent Killing technique from the bat, meaning Hidan would have a slim to non chance of ever getting a hit on Zabuza, unless he went ballistic and ran around swinging his blade randomly and with a helluvah lot of luck hit Zabuza despite all odds... (Come to think about it, isn't that actually his ordinary fighting-style?)
But well, if Zabuza had no knowledge about his abilities, and went into direct swordplay with Hidan, as we all know, one cut and it's more or less over, unless he figures out his ability in the last second and blows him away from the circle with a Water Dragon Missile or something... Though that'd damage him too, it'd be better than instant death from Hidan's curse.