You Do Need power plug adapter while traveling from Greenland 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 Greenland are C, E, F and K. This is how they look like.

Greenland

In Greenland, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K

Cayman Islands

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

Type A

Type B