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

Here is Why You Need An Adapter

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

Mauritius

In Mauritius, 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