You Do Need power plug adapter while traveling from Saint Martin 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 Martin are C and E. This is how they look like.

Saint Martin

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

Type C

Type E

Cocos (Keeling) Islands

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

Type I