I can share my insight into how things regarding weather events have gone on in the past (Mitch, EmIly, Wilma and Dean) from my experiences.
Cozumel does an excellent job in management, and preparations prior to a hurricane. There are more shelters (from my observation) then in previous years.
Preparations are made If there is a potential of a weather event. Shelters are stocked, hotels, ferries, and airlines are put on alert. As in the case of Mitch and Dean, all preparations were made, and the storms turned at the last possible moment, and all was well.
In the recent cases of Emily and Wilma, the oceanfront hotels were evacuated, and secured. The guest are told about the shelters, and grabbed blankets and pillows from the hotels. Most headed to the airport. They returned to the shelters when they could not secure a seat.
The airlines waved the change fees if you could secure seating.. Heading to Cancun prior to the ferries departing was/is an option, however, lots more people all trying to leave at the same time.
If a storm is imminent, the ferries are taken off the island, and the last plane leaves. Not all storms are major,or equal, and depending on the category, it really is a personal choice as to go or to stay.
Those who did stay pitched in to help get Cozumel back on it's feet. For Wilma, it was a huge task, but Cozumel received it's first ship in only 3 weeks post hurricane. That was some effort by all.
The island is well prepared for these types of events. Everyone was safe, perhaps not as comfortable as anyone expected, but safe and had food, and water provided.
The Convention Center next to Chedrui's has been completely renovated, and is almost ready to open.
If I needed to seek shelter, that would be my first choice. There are smaller hotels away from the beach area that is also good options.
The point of sharing this is not to cause fear, but only for your awareness, and what your options are.