There are taxis of all sizes and you might have to wait for a van, but I suspect getting the scooter to Chankanaab wouldn't be a problem. Once inside Chankanaab, there is a very firm trail that a scooter would have no problem with. Many areas of the park are very accesible and I believe that everyone would enjoy them.
Even certain parts of the beach are accessible. One beach club that comes to mind as being very accessible is Nachi Cocum. Easy arrival, easy entrance and a huge covered area to enjoy....but most of the beach clubs would offer the same.