If there was a radio with push button up / down channel selection but no a way to scan stored memories, could a simple circuit be added to perform a scanning function to find active channels?
You won't place this circuit in the microphone.
Such a circuit would need to be IN the radio, for access to other analog and/or digital signals, such as the squelch line, as mentioned by Dale, W4OP.
There were a large number of these adaptations in 1970s amateur literature (NE555 and discrete transistors) for crystal VHF/UHF radios to provide a scanning function.
PULL UP the schematic for the radio you desire this function .... That will be a starting point.
You need to UNDERSTAND how your current radio works, BEFORE modification -- otherwise it's an ill-advised hack.