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

Here is Why You Need An Adapter

The outlet and plug type used in Azores are B, 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

Azores

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

Type B

Type C

Type F