where is this switch located, on the inputs to the amps, or on the outputs to the speakers?
i built a simple switch that selects one of four line level outputs (4 sound cards) and passes it to a line level input on an amp, I'm able to switch between them with no pops, in fact I can switch them so fast, they sort of all run together in a weird way ... However, I'm using an electronic switch - an analog multiplexer, not a mechanical relay
if you're interested in building yourself a new switch, try searching for 74HC4052 (or 4051), there are lots of audio projects based around these parts.