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

Here is Why You Need An Adapter

The outlet and plug type used in New Caledonia 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

New Caledonia

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

Type C

Type F