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

Here is Why You Need An Adapter

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

Western Sahara

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

Type C

Type E

Cook Islands

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

Type I