I am cave certified, but my wife won't have anything to do with them.
MNawman, my story is similar: I'm cave certified and its my husband (a retired US Army Special Forces colonel!) who won't have anything to do with them!
I dove Arrelito del Paraiso (sp?), a very nice cave toward the south end of the island, with German Yanez in December while I was there on a reef-diving trip. Ditto all the positive comments about German. He will have doubles for you to use. I brought my own BP/wings and cave reg set. The only fins I brought were my ScubaPro Twin Jet split fins with spring straps. Not what I normally use for cave diving, but German was OK with them.
The cenotes on Coz are not as decorated as on the mainland. Thank goodness because there is more risk of klincking your tanks against the ceiling in a cenote than in the Florida caves where I usually dive. There are 2 reasons for this: 1) the salt and fresh water layers in the cenote (halocline) and 2) you will be in double AL80 -- not steel -- tanks. Both of these factors will challenge your bouyancy skills. If you transition from the fresh water to the salt water layer you instantly become a little more bouyant. When you are in one layer, looking up, the distortion of the layer above you prevents you from seeing the ceiling. Sometimes there is no way to tell if its 2" or 20' from your tanks. You have to stay close to the floor without silting up the place. Add to that the more pronounced change in bouyancy as you breathe down your AL80s. Last month was my first time in a Mexican cenote and I was grateful to practice in one where there was less risk ruining decorations.
Be sure to stay a little to the side of of the diver in front of you -- out of his "prop wash" and not directly behind him. Finning in a halocline expands the area of visual distortion. Its like looking through poured glass and can be a little unnerving to the uninitiated. If you are to the side of the diver in front and not where the salt/fresh water layers meet, you should have gin-clear viz.
That said, the experience was fantastic! German pointed out some anemonies and sea stars that he said are found nowhere else in the world except that particular cave.
My reef-diving buddies on the trip thought I was insane. But I just grinned and was grateful to have gained admission to such a wonderous place.