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

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) 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

Cocos (Keeling) Islands

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

Type I