Measure an optically averaged patch of sky - use an out of focus image of a circle a few degrees in diameter. For reference, the moon subtends half a degree. Derive RGB numbers for the measured sample. Translate the RGB(sky) to RGB(leds) by use of a 2x3 matrix that you derive from experiment. Display the resultant color on the RGB LED.
Beware, people perceive colors differently. This means the translation matrix will be different for different individuals. The hard part is making it an ambiguous enough matrix to convince the largest fraction of observers.