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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Martin are C and E 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 Martin

In Saint Martin, outlets of type C and E are in use.

Type C

Type E