For the on/off indicator, the size and color makes no difference. It doesn't affect the sound. You can also adjust the resistor in series with the indicator led to change the brightness.
There are other times when an LED is used as part of the circuit and does affect the sound. This is in some distortion/od pedals, where the leds act like clipping diodes. The color will definitely matter since different color leds have a different forward voltage. So socketing and experimenting with these is recommended. The size often doesn't have and impact on the forward voltage, but it doesn't hurt to check.
Other circuits used leds with light sensors (ldr) to affect the sound. phasers, vibes, tremolos, compressors, etc can use leds like this. In these circuits both size and color can affect the sound, because it can change how the ldr detects the light. The forward voltage can also affect how bright the LED lights up, which would also affect the sound.