listen here: Dropbox - 180622_0031.wav - Simplify your life
What makes you think this noise is a hum? A hum is a 50 to 120 HZ sound derived from the mains.
It sounds more like EM interference from other parts of the system. Is the clicking synchronised with anything like flashing LEDs or commands to the player?
Things you can try:-
- Star wiring on the power rails. That is the power and ground connected only at one point not chained.
- Reduce the impedance of the audio inputs, by putting a resistor to ground on each input.
- Add some more aggressive decoupling like a Pi filter shown on the last circuit of this link.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
However, mixing digital circuits and analogue ones is not easy, it is not like building Lego blocks. A lot depends on physical layout. Can you post some actual photographs of your system.