If you are ever feeling like burning down your apartment ;), the route I'd take is buying a 5-20p extension cable, cutting it open, and splicing in a 120V switch into the middle of it. You can find a few smart switches that fit that bill for whatever relay tech you are interested. It's non-invasive for the AC unit and can be quickly removed.

There's only 3 wires to deal with as well so it's not THAT scary to make your own cable (but I'd understand why you might feel differently).

> It can handle the full 15 amps of the circuit safely.

OP would need a more beefy relay for an AC unit. 20A minimum, but honestly a 30 or 40A relay would be warranted as AC units have a pretty large "spike" when they turn on which generally exceeds the amp rating of their circuit. It's short enough to not trigger a circuit breaker, but it's something to be aware of when designing things like relays.

I'm fairly certain those exist. The "click" that a car charger makes is a commuter (sp?) (basically a relay) connecting the car to voltage. Mine handles 40 amps.