Zabuza will not underestimate an akatsuki member and will try to kill ASAP once he finds out his fame and power! Just by the cloak alone they where he could know he is one of the best. But with out intel he would test Hidans combat with that scythe.. Then that's where he unfortunately might lose.
If he doesn't simply just blitz and decapate and instead try to engage in weapon clashing (who has the biggest sword. Lol) he will lose since Hidans weapon is design to exploit the kink in an opponents armor.
It's up in the air if he doesn't know Hidans group fame, but if he knows akatsuki he will kill no diff. Both are kinda the truth when it comes to cqc killing. Haha
Yeah, it all depends on the intel and if Zabuza is aware of Hidans status.
With intel on his abilities, the ritual is out of the question. His ritual trigram (blood) will be washed away no difficulty with Suiton from Zabuza if he uses it on the bridge and he obviously can't use it on water (since this fight takes place on Great Naruto Bridge) so Hidans only hope would be to outlast Zabuza (which he most certainly could, no doubt) because none of his Suitons apply enough blunt force to put Hidan down.
However, given the fact that Zabuza can use Suiton Bunshins, he can easily let them engage Hidan so Hidan won't get his blood (not like it matters anyway like I said Suiton washes his ritual trigram off the bridge) and Hidden Mist makes it worse for Hidan. Then we still have the Suiton Prison that can immobilize Hidan so a Zabuza bunshin could decapitate him.
So yeah, Zabuza can certainly win but only with intel on Hidans dangerous abilities. This is considering Zabuza doesn't burn out of chakra too because I'm not sure if he will. Hidan never gets tired so he could probably outlast.