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

Here is Why You Need An Adapter

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

Botswana

In Botswana, 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