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

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Isle of Man are C and G. This is how they look like.

Isle of Man

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

Type C

Type G

Cook Islands

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

Type I