Will both amplifiers function properly without speakers? Do you let the amplifiers continue working without speakers? Some amplifiers aren't happy if/when you suddenly remove the speakers.
I would think something like turn off / unplug amplifier 1 , wait 1s, switch relays, wait 1s, turn on amplifier 2 would make more sense. So that means either a microcontroller or some time delay circuit / logic.
With a microcontroller, you would also be able to use bi-stable relays, so that once they're switched, you don't need to keep sending power to the relays.
Actually even without a microcontroller, you could probably have a slide switch [amp 1] -- off - [ amp 2] or something like that, and depending on the slide switch position you would reverse the polarity to the relays and flip them as needed.
I'd also add a capacitor at the input, something like 100uF 25v... also don't be cheap and add a diode on each relay primary winding.