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

Here is Why You Need An Adapter

The outlet and plug type used in South Korea is F 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

South Korea

In South Korea, outlets of type F are in use.

Type F