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).