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

Here is Why You Need An Adapter

The outlet and plug type used in Åland Islands are C and F 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

Åland Islands

In Åland Islands, outlets of type C and F are in use.

Type C

Type F