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

Here is Why You Need An Adapter

The outlet and plug type used in Guam are A and B 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

Guam

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

Type A

Type B