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