You Do Need power plug adapter while traveling from Papua New Guinea 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 Papua New Guinea is I. This is how they look like.

Papua New Guinea

In Papua New Guinea, outlets of type I are in use.

Type I

Cayman Islands

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

Type A

Type B