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

Here is Why You Need An Adapter

The outlet and plug type used in Denmark are C, E, F and K 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

Denmark

In Denmark, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K