You Do Need power plug adapter while traveling from Antigua and Barbuda to Cook Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Antigua and Barbuda are A and B. This is how they look like.

Antigua and Barbuda

In Antigua and Barbuda, outlets of type A and B are in use.

Type A

Type B

Cook Islands

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

Type I