You may be stuck with it.

Some switching systems use J-FET transistors as switching elements so that the selected channel can be turned on slowly, like rolling up the volume knob. This makes for silent switching.

Mechanical switching will simply disconnect one channel and connect the other one. Any transient voltages produced by this process will get sent through the amp, coming out the speakers as a 'click' or 'pop' sound.

A phone call or e-mail to Carvin can probably resolve what kind of switching circuit is used. If they use transistors for channel selection, there should not be any clicking. If they use relays, or mechanical switches, there will always be at least a bit of noise produced.