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

Here is Why You Need An Adapter

The outlet and plug type used in Greenland 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

Greenland

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

Type C

Type E

Type F

Type K