transfer switch
either manual toggle or a relay
double pole, double throw.. total of six contacts
load side aka outlet circuit goes on the center pair/common contacts
the two input methods go on the other two pairs
hot/neutral pair, on each of the two input sets
the switch/relay .. chooses which power is used
opening an outlet cover is not the problem
its getting the power into the wall behind the outlet
or to the junction someplace where the romex from the outlet is connected to the hot feed from the panel
IF you can pull a new circuit from the inverter to the area of the outlet
you can then use a 20amp DPDT toggle switch to choose between the two power methods, existing from panel or the new circuit from the inverter
thing is if you can pull wire there, why mess with the switch
just mount another outlet right there connected to the inverter
then all you have to do is move the "coffee maker" plug from outlet to the other