You Do Need power plug adapter while traveling from Equatorial Guinea to Cook Islands.

Here is Why You Need An Adapter

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

Equatorial Guinea

In Equatorial Guinea, 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