Sorry but travel between Caye Caulker and Cancun by air is not realistic.
There is a way, go via Belize International to Tikal (Flores, Guatemala) and then to Cancun.
Another way is to go from Caye Caulker to San Pedro, Ambergris Caye then to Corozal by Tropic or Maya Island Air. Cross the border using taxi or public transportation into Chetumal, Mexico. Then take a flight from Chetumal to Cancun using AeroCaribe.
None of these methods are cheap.
The bus between Cancun and Chetumal takes about 6 hours using Primera Clase (First Class) buses. This is the most inexpensive route and very well traveled. Lots of buses each day.