Guido,
"but do I need a switch between the channel output at the receiver?"
Yes, its called a switcher. Plugs into the channel, takes information from the channel, and switches power according to those instructions. Receiver outputs are just information and effectively have zero power handling.
John,
"Hello, I don't know if your problem has been solved. My LED is broken. Now I need to replace it. Please help me choose a device that suits me."
Mostly a case of getting one the same size, shape and colour. Provided that the circuit supplying it was OK, and the replacement is fitted the same way round (the D in LED stands for Diode, indicating that they don't like having power the wrong way round), it will work. If the circuit supplies too much current, the new one will fail as well, same if the power is reversed. Without knowing the original device, its size and mounting and what circuit was controlling it, suggestions must be very general.
Tim,
A voltage reducer might help the choice of resistor, but running an LED without a ballast resistor is placing total reliance on pure luck. That luck will be helped by the possible inability of the voltage regulator to supply too much current. Things like LED key fob lights rely totally on the internal resistance of the button cell to do this job.