Kind of switch required to select between power sources
Transfer Switch
A double-pole double-throw break-before-make is essentially what you need. But there are devices designed exactly for this. Transfer switch is the term.
Large transfer switches are used in buildings to transfer between backup generator and utility power. You just need a small one - ~ 20 Amp - to transfer one circuit, but the principle (and the terminology) is the same. Depending on how your RV electrical supply is setup, you may be able to put a transfer switch inline with the one circuit for the microwave, or you may want to install it with the main breaker panel. If you install it with the main panel then you have to figure out how to separate different circuits so you don't overload the inverter when you flip the switch, though adding some LED lighting or other small loads would probably be fine.
There are automatic transfer switches, but those are typically for unattended switching to generator when the power goes out, but there is no benefit to that here, and in fact you would probably NOT want it on automatic as there will be times when you don't have shore power AND don't want to turn on the inverter either.