Do you care about pop? With a modern amp, you shouldn't hurt it by disconnecting its output, however it might sound pretty bad when you connect to the active amp.
Thise are relatively low powered amps, so I would not be real concerned about it. If they were over 50W, I'd be concerned. Ideally, you should have a resistor in place of the speaker for a large amp (8 ohm wirewound rated at or over the max wattage). [Two if this is stereo].
With more complex switching, you could set this up so that when you switch it, the resistor(s) are put in place of the speaker.
Since you said you will only switch is rarely, just make sure both amps are shut off and save the cost and trouble of resitors and complex switches or relays. It shouldn't be too hard to remember to turn off the amps, (unless you've been drinking alcohol ). You could also get more complex, and have multiple relays, which turn the power off to the amp you are not using, and turn on the one you are using...
None of the amps nor speakers are colocated. So, getting to the inputs of the amps is "expensive". Otherwise, I'd just fade out, flip switch then fade in.
My question tries to address the case where I can make *no* assumptions as to the signals present at the switch (i.e., arriving from two amps operated without regard for the switch's presence).
[I can obviously design something that will safely operate regardless of the operating conditions -- but at additional cost]
How stable are the amplifiers with no load connected?
If the amplifiers will tolerate no load (or you can put a load resistor low enough to ensure stability and high enough not to require a serious power rating) then apart from a click/pop when you do it probably not much. My TV does this to the HiFi when it is switched on since the external optical DAC becomes live before the TV finished booting.
The click originates from zero to first random sample of signal sharp transition.
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