As said, that 'pop' is a 'feature' in some amps and can't really be helped by no other means than adding a mute circuit.
If the supply caps were dead there's a fair chance that some caps have become leaky and are now bleeding small amounts of DC to a wrong place, which during the power down might cause a discharging phenomena that is 'bled' to the signal path and fed to the speaker as the 'pop'. So other than the first suggestion of checking out the delay circuit (assuming one even exists), you might try looking out for DC offsets that seem out of place and which might cause the pop when power is turned down. The volume control is not always right before the PA, though. Hence turning down the volume control can often decrease the 'popping' significantly. The effect is magnified if this happens in the early stages of preamp after which there is typically tons of gain. The pop originates from the AC component of charging/discharging the capacitors 'finding its way' to the signal path. Many amps don't have one, though, and the standard feature of these is to 'pop' annoyingly. If yes, check out that it works flawlessly. Does it have a delay/mute circuit built-in? (Relay in output or FET in PA input or something like that).
