Compatibility summary
You will need a travel adapter in Cayman Islands; plug types used there differ from Brazil.
Plug comparison
Brazil plug types: C N
Cayman Islands plug types: A B
There is no common plug type between Brazil (C N) and Cayman Islands (A B). You need a travel adapter.
Voltage comparison
Brazil: 127V, 60Hz
Cayman Islands: 120V, 60Hz
Voltage difference is within a range many devices tolerate; check your appliance label.