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

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands is I and in Madeira are C and F. This is how they look like.

Madeira

In Madeira, outlets of type C and F are in use.

Type C

Type F

Cook Islands

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

Type I