Replace mechanical switch with relay
You say the push buttons are non-existent? I'm assuming they are rubber/graphite buttons, which work just like push buttons. I'm also assuming that the buttons pass very small currents and voltages. You want to measure to make sure.

In either case, yes, you can simply replace them with mechanical relays. Of course you want to use relays which work at 24V coil voltage. Size wise, reed relays are pretty small, but you can also find SMD relays that are small that you could solder without issues as well. The diode is to protect your output if DC. If AC, you should get a relay meant for AC coil voltage instead of DC. 







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