For colours, there's a BIG difference in reproduction on screen (RGB) and in print (CMYK). There are colours that can be represented in one colour space (bright oranges and greens in RGB) that simply don't exist in the other colour space.
But back to OP's problem.
My approach would be:
- find an RGB sensor. Find the spectral response in the data sheet of the three colours.
- find three LEDs, one red, one green, one blue, with a spectrum that matches the sensitivity of the sensor. Bonus for finding them in a single package.
- read the sensor, use the values to drive the brightness of the LEDs.
This should (in theory, at least) give a quite close representation of the sky colour. Some correction factor on the brightnesses may be needed (LEDs may have a different response than the sensor).