"pass through" inverter

cptdondo

I have a bit of a weird situation.  I need a small (300W) inverter to power a wifi access point and a small TV when grid power is not available. 

I want to be able to turn on the TV and wifi AP via a switch.

Here's where I'm running myself into circles:

I also want that switch to work when plugged in to 120VAC, and I also want that switch to turn on the inverter but only when I'm not connected to the grid.

So I'm looking for a "pass through" inverter; something like an inverter charger but without the charging circuit.

Does such a thing exist?  Or will I have to rig something with an ATS and some relays?