You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to Saint Kitts and Nevis.

Here is Why You Need An Adapter

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

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I

Saint Kitts and Nevis

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

Type D

Type G