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

Here is Why You Need An Adapter

The outlet and plug type used in Réunion 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

Réunion

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

Type C

Type E