Replace some LEDs with Diodes
Without a schematic it's pretty hard to be sure, but 'nine times out of ten' the LEDs could be snipped out with no effect on the functionality. Replacing them with diodes would stop the light emission, but would almost surely use more energy, or could even possibly damage the circuitry. That's because LED driving circuits usually present a fairly fixed voltage with a resistance that's designed to cause a certain current to flow through the LED. 

For example, a 3.3V circuit driving a 2.4V LED to 7.5mA would use a 120\$\Omega\$ resistor. If you replace the 2.4V LED with a 0.7V diode it will draw almost 22mA or almost 3x the current (and therefore, since it's all supplied by 3.3V, almost 3x the power, and over a given time period, 3x the energy).