the Chichen Itza plane is a twin prop plane, and not very big, maybe a 40 seater? The altitude they fly at is fairly low sence by the time you get to altitude, it's time to decend. If your question is if it's safe to fly after a week's diving? I would think the 12 hr. rule would still apply, but I'm not a doc.
We did the C.I. flt. a few years ago and it's the only way to go from Coz, driving and bus tours take too long to get there. A 45min. ferry ride, 1/2+ to rent the car or loading on the cattle bus, THEN a 3 1/2+ hr. drive/ride to the archeological site...it's too much.
The tour guide we had at the site was very good, educational and personable and the site it's self?...well it's just awsome, get the camera ready! I've been there twice and hope to get back in the next few years.
I don't think they have any locker facilities at the airport, none that I've seen anyway. They have been renovating the place over the past couple years, maybe they have put some in that I haven't seen.
You could try checking your luggage early with the airline you are flying home on, if they have a gate open that early. Your luggage may go on an earlier flight and be waiting for you when you get home. What airline are you flying? If it's one of the majors, they may have a gate open, if it's a charter, they may only open gates a couple hours prior to flt. time.