Wiring a light to activate via relay
What you are describing is a bit of a hack up. Ideally, one would distribute the information in some other way. Might you consider locating the machine running the audio signal closer to your lights?

Anyway, if you want to do it the way you describe, then I would avoid having the current for the LEDs flowing through the long wires. Instead, use something like this with a mosfet:







simulate this circuit &ndash; Schematic created using CircuitLab

Not sure how long of a wire you can actually get away with.