You Do Need power plug adapter while traveling from Saint Kitts and Nevis to Cook Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Saint Kitts and Nevis are D and G. This is how they look like.

Saint Kitts and Nevis

In Saint Kitts and Nevis, outlets of type D and G are in use.

Type D

Type G

Cook Islands

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

Type I