You Do Need power plug adapter while traveling from Cook Islands to Western Sahara.

Here is Why You Need An Adapter

The outlet and plug type used in Western Sahara are C and E and in Cook Islands is I. This is how they look like.

Cook Islands

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

Type I

Western Sahara

In Western Sahara, outlets of type C and E are in use.

Type C

Type E