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

Here is Why You Need An Adapter

The outlet and plug type used in Kuwait is G 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

Kuwait

In Kuwait, outlets of type G are in use.

Type G