But a plug in one actually is a really good idea. I suggested at one stage that the air con should be extended into the froot. Useful for perishable groceries for instance. I think Jaguar used to do it and may still be doing it, for all I know.
To get power down there would not be hard, actually. The fuse boxes are directly above the microwave. Lots of appropriate connectors available at boating electrical suppliers. One excellent brand is Bulgan. Installed correctly, they are correctly polarised every time. I have installed them on my boat in the past. The plug screws onto the socket so it cannot jar loose. This is, I think a DIY install.
Regarding the fridge, Waeco make them, but I wouldn't know if they would make one small enough!
Waeco 31L Compressor Fridge Freezer - Coolers | Harvey Norman Australia
I suppose I need to go get the tape measure out!