Is this device run from a wallwart, not from power coming directly from the outlet? I doubt that the circuit will work properly in all stages with a 9v battery. I don’t believe they would use different voltages for the RF circuit and the relay latch circuit, it would be unnecessary complex and expensive. But you could try to use two 9v batterys in series (18v), which might work. Just don’t expect two 9V PP3s to keep the relay closed for a very long time! ;)