Hey Eden,
Yes they absolutely have a cook available. You can asked them to prepare any groceries you purchased (or fish you caught

), or ask them to purchase groceries for you. They even offered a candle light dinner in the cave (unfortunately only Daisy knew that, Ninja can tell you how panicked I was before we left, because I booked too late and it was really hard to find a place that would take reservations for our anniversary dinner with only two weeks notice (find out how it turned out in a later episode - only here on negril.com!))
Alternatively you can order anything from the LTU-menu and have it brought to you. Anything you order can also be put on your tab at Villa Sur Mer for convenience.