Nope. Zabuza wins this one via drowning Kimmimaro. As you said Zabuza has knowledge on his abilities so he knows sword slashes won't work.
-Kimmimaro's reflexes are useless if he actually can't see the attacks. Kakashi with sharingan precog was barely able to react to the attacks on time
-Zabuza's sunshin (travelling speed) is > Kimmimaro's. And agility and reflexes are nullified by the fact that hidden mist simply hides Zabuza's attacks.
-Kimmimaro is agile enough to dodge any frontal overwhelming attack, but once get got trapped in a surprise attack (hence Gaara's sand on his feet) he couldn't react on time. Meaning Kimmi doesn't have good feats on reacting to attacks he can only see on the last second.
-If kimmimaro can't locate Zabuza to attack him, he could use bone forest (that covers the hole area) to make sure he hits him. But Zabuza's speed feats and the fact that he was able to hear Kakashi's ninken dogs underground guarantee that he'd be able to jump away on time (since p1 Gaara reacted to it, there's no way a shinobi that kept up with Kakashi in CQC wouldn't react). Once he jumps, he can find a safe spot between the bones and attack kimmi from a far distance with water bortex ot water dragon(let's not forget kimmimaro still doesn't know where Zabuza is)
The battle is simple and doesn't have a lot of details. Zabuza is faster (sunshin wise) so he can definitely dodge any incoming attack from Kimimaro, since Kimmi won't even know where to attack since he doesn't see Zabuza, not to mention Zabuza can use clones as distractions, so definitely no way Kimmi lands a hit on Zabuza inside the mist.
Kimmimaro's reflexes and agilities are not useful against attacks he can't see coming (hence he didn't have a way to sense Gaara's surprise attacks) and if Kakashi couldn't react to them with sharingan precog, then forget about zabuza.
If kimmi uses bone forest i already adressed Zabuza's counter. Then kimmimaro gets drowned on water prison, unless someone proves that Kimmimaro's bones can pierce something harder than steel.