I've summarized the most relevant customs regulations below (although I encourage you to read them for yourselves at their website
Cayman Islands Customs - Grand Cayman, Cayman Brac, Little Cayman).
Regardless of whether you are under the duty-free limits or not, all visitors must declare all gifts, foods, spirits, liquor, tobacco products and any other items in their possession, other than their normal wearing apparel, personal effects/toiletries and articles of personal adornment which are reasonable for the time of the intended visit to the Cayman Islands.
Regarding visitors' duty-free limits: Baggage and household effects for visiting tourists are generally duty free if they are either consumed or used up during your stay, or taken with you when you return home. (Residents returning to the island can bring in $350/person of goods purchased while off island before owing duty.)
Further and more specifically, you can bring in duty-free:
1) (if you are over 18) up to 1 liter of spirits or 4 liters of wine or 1 case (not exceeding 9 liters) of beer; and up to 200 cigarettes or 250 grams tobacco (roughly 25 cigars)
2) Clothing, articles of “personal adornment,” and any other personal effects the customs officer deems reasonable for the period of the intended visit.
3) medical devices
NO guns, drugs, pornography, or turtle meat may be imported (just in case you were thinking.... )
Regarding (non-turtle meat) perishable products; from the CI website: “Perishable food items imported into the Cayman Islands requires a certificate of wholesomeness from the country of purchase or origin and is subject to inspection by the C.I. Department of Agriculture on arrival. An import permit issued by the C.I. Department of Agriculture is also required.”
However, in another place on their website it says that small quantity of meats (up to 25Ibs.) arriving in passengers baggage from the approved countries [see below] may be permitted without an accompanied Certificate of Wholesomeness, if such meats are pre-wrapped under a brand name and has the Official Seal of Inspection of the country's Meat Inspection Authority. Secondly, if such small quantities of meats were purchased from a licensed shopping outlet and are wrapped by the outlet. Such meats may be permitted entry into these Islands at the discretion of the approved Inspector at the port of entry, providing adequate proof of such purchases from licensed establishments can be provided by the arriving passenger.
APPROVED LIST OF COUNTRIES FROM WHICH MEATS CAN BE IMPORTED:
United Kingdom, Northern Ireland - Swine products only are allowed with specific certification, form 5773 EHC.;
USA, Canada, CARICOM States, Australia and New Zealand - all types of approved meats in these countries are allowed.
Costa Rica, Nicaragua and Honduras -meats of swine and ruminants only are allowed with a proper certificate of inspection. (Boneless meat only from Nicaragua).
Finally, given that small amounts of meat are OK, I am sure small amounts of other perishables are OK as well. We almost always arrive with small amount of fruit, baked goods and other incidental perishables with no problem.
And finally, finally, when in doubt, DECLARE!