How big capacitor would be needed to get rid of static in radio?
Just buy and install a noise filter. That will work to subdue static. If the lights are giving off RF interference that problem isn't remedied with a capacitor. You need a notch filter to control noise at the particular frequency the light produces.
Run separate wires to both FROM & back to the battery.Keep the wires well apart.. Check the grounding of the aerial.
If you have static on an FM radio then there is something seriously wrong with that radio. Static and niose in general is AM which stands for Amplitude Modulation. FM is frequency Modulation and it has circuits which automatically block AM.