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

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Åland Islands are C and F. This is how they look like.

Åland Islands

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

Type C

Type F

Cook Islands

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

Type I