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