Wikipedia, "Economy of the Cayman Islands" section. If the page is correct and tourism is 70% of their GDP, then they are in a worse position to weather the storm than other islands such as The Bahamas for example. Only approx 51% of The Bahamas' GDP is dependent on tourism.
"Tourism is also a mainstay, accounting for about 70% of GDP and 75% of foreign currency earnings." - Cayman Islands, according to the world fact book, CIA