Dual rail power supply for audio needs to drive LED too, unsure of design approach
Drawing a small amount of DC current from your supply will have no effect on the audio. Your headphone amplifier will itself draw DC power from the supply to use internally. 

Just use a series resistor. Since you have such a high voltage, pick an efficient LED and keep the current relatively low to save power- 1mA may enough for a good LED. 

By the way, in your question, the word you want is affect.