You Do Need power plug adapter while traveling from Cayman Islands 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 Cayman Islands are A and B. This is how they look like.

Cayman Islands

In Cayman Islands, outlets of type A and B are in use.

Type A

Type B

Cocos (Keeling) Islands

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

Type I