Compatibility summary
You will need a travel adapter in Cook Islands; plug types used there differ from Mexico. Voltage differs by more than 20% — a voltage converter may be needed for some appliances.
Plug comparison
Mexico plug types: A B
Cook Islands plug types: I
There is no common plug type between Mexico (A B) and Cook Islands (I). You need a travel adapter.
Voltage comparison
Mexico: 127V, 60Hz
Cook Islands: 240V, 50Hz
Voltage converter recommended (Mexico 127V vs Cook Islands 240V).