How can you wire a 555 timer to gradually decrease sound volume?
Honestly, one of the least fussy solutions would be a small MCU and a digipot. Specifically, a log digital potentiometer designed for audio (so that it switches on zero crossings), and just about any microcontroller. 
Most digital pots are controlled via I2C (or occasionally SPI).

You can trigger the "fade" however you like (button, etc), and you have very good control of fade length and linearity. You can even do stereo with nearly gain-matched channels (there are digipots specifically for stereo audio).

This way, no analog weirdness, programmable fade characteristics, flexible triggering (you still haven't said how you want it to trigger), and basically two parts (plus a power source and a smidgen of passives).