I'm not a cave diver and don't have any desire to be, but I have done some cenote dives as a AOW diver.
Like with any other dive, it is ultimately your responsibility to only do dives you are comfortable with, regardless of what the minimum training requirement for the dive may be. Cenote cavern dives are not for everyone. (Same as night dives, swim throughs and deep dives are not for everyone). You cannot do a cenote cavern dive on your own unless you are cavern or cave certified. As an OW diver you can do them with a qualified guide. If you don't have near perfect bouyancy skills, or have any issues with being in closed in or dark spaces, don't even consider one of these dives regardless of your cert level or how good the guide is.
Technically, the cavern sections of a cenote cave system will always have natural light visable and be within a specific distance to an exit point (sorry, don't recall the exact distance off hand). Choose a reputable, trained, cave guide who makes safety a priority and you will have a safe and unique diving experience.