You Do Need power plug adapter while traveling from South Africa to Cook Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in South Africa are C, M and N. This is how they look like.

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N

Cook Islands

In Cook Islands, outlets of type I are in use.

Type I