Compatibility summary
You will need a travel adapter in Cook Islands; plug types used there differ from Japan. Voltage differs by more than 20% — a voltage converter may be needed for some appliances.
Plug comparison
Japan plug types: A B
Cook Islands plug types: I
There is no common plug type between Japan (A B) and Cook Islands (I). You need a travel adapter.
Voltage comparison
Japan: 100V, 50Hz
Cook Islands: 240V, 50Hz
Voltage converter recommended (Japan 100V vs Cook Islands 240V).