Presumably your switch has 3 terminals. In, Out and GND
If so then the GND connection is used to provide a 0 volts point for the LED circuit. (the LED will have an in-built current control resistor) The In connection will be commoned with the LED
Simply tie the GND connection to the Out connection.
When switch is closed the In and Out will be at the same potential so LED will not illuminate.
When the switch is open, the Out connection will be connected to the zero volts line via the load (your relay ?) and sufficient current will flow to illuminate the LED - but not enough to activate the relay.
So, no need for transistors !