You Do Need power plug adapter while traveling from North Korea to Cayman Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cayman Islands are A and B and in North Korea is C. This is how they look like.

North Korea

In North Korea, outlets of type C are in use.

Type C

Cayman Islands

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

Type A

Type B