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

Here is Why You Need An Adapter

The outlet and plug type used in Georgia are C and 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

Georgia

In Georgia, outlets of type C and F are in use.

Type C

Type F