Compatibility summary
You will need a travel adapter in Saint Kitts and Nevis; plug types used there differ from South Africa.
Plug comparison
South Africa plug types: C D M N
Saint Kitts and Nevis plug types: A B G
There is no common plug type between South Africa (C D M N) and Saint Kitts and Nevis (A B G). You need a travel adapter.
Voltage comparison
South Africa: 230V, 50Hz
Saint Kitts and Nevis: 230V, 60Hz
Voltage difference is within a range many devices tolerate; check your appliance label.