It may depend how much longer you will be in the area, ie. if you lose it on a Friday and you are leaving Monday or Tuesday, that is cutting it close to have one sent to you.

Be sure to notify your bank that you will be using your card in Jamaica before you go on vacation.

Once, maybe twice I have had cards replaced while in Jamaica. I have also had an ATM withdrawal credited back to my account when the money wasn't dispensed. That one took a little more work and the input of my bank, but it got resolved!