I just retired from ac work after 30 years. have your sheet metal guy build a box for it. The actual problem for me is wiring it so you don't have to plug and unplug a cord when using it. A transfer relay is kindof special and that is one way of eliminating the plug dance. It has n/o and n/c contacts and a 120v coil, most are open relays.
That's the reason I choose a inverter with a transfer switch built in. I have 7 wires, 120 in 120 out and +/-12v. every thing is switched inside the box automatically when the generator's running or when the external power is connected. the inverter switches to line voltage when either is connected AND charges the battery.
This is what I have but it's more than your inverter you have in mind, it's totally automatic