Simple OR circuit with 2 inputs
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) Diode circuit. (b) Relay circuit.


  Would a diode or circuit work?


A diode circuit would work but would result in a 0.7 V drop in voltage.

The alternative is to use a relay to prioritise one supply over the other. Figure 1b shows that V4 will energise the relay and supply the output. When V4 is off V3 will supply the output. The relay contact will not drop any voltage but the relay coil will consume some current.