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