> mono signal between 24 different outputs. ... clicking is not acceptable.
First, ensure no stray DC at inputs or outputs.
Then.... if you hard-switch in the middle of a wave, it is still going to "click".
You can try zero-crossing detection, which waits for the audio to cross zero. Several chips have it built in, but all are way over-complicated for plain switching duty.
Or you can "fade". But to do this requires a real fader (pot, VCA, or VCR) that has a clean "dim" range between off and on. Mechanical switches can't do that, and it ain't easy in FETs or opto-Rs.
And for 24 outs, it needs to be easy.
Look at the soft-switch chips. SSM2404 is four switches that fade up/down in 5-10 milliSeconds.
http://www.analog.com/UploadedFiles/Data_Sheets/36658935ssm2404.pdf
The obvious thing to do is put one unit in series with each output (power-amp inputs?). The on-resistance is very low, no problem there for 10K or 100K loads. The off resistance is high enough to give 60dB-80dB "off"... on a test rig. However if you have long lines to power amps, the open switch lets all kinds of crap leak into the cable. Test this plan in mock-up before you try it for real. Cures would be op-amp buffers on each output, or a second switch to short the "off" inputs when not in use.
To turn a switch on or off, bring its control pin to +3V or 0V. Simplest would be a 1-pole 24-throw switch, wiper through 1K to +5V, each throw to a switch input with 5K to ground. Either rotary or interlocked pushbutton would force 1-of-24 operation. If multiple outputs at once are not illegal, just use a toggle or push-on/push-off switch for each position.