You Do Need power plug adapter while traveling from Cook Islands to Isle of Man.

Here is Why You Need An Adapter

The outlet and plug type used in Isle of Man are C and G 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

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G