Joe, those switches will work fine on DC until you try to open a circuit with 10 or 15 amps of inductive load. Then it will weld shut because there is no zero crossing to put out the fire.
You can mitigate that with a diode across it.
I hope you don't mean the yellow plug is the output of the inverter.
I am still concerned with mixing 12 volt and 120 volt receptacles using the same type of plug. I would use "lighter plugs" for all of my 12 volt stuff. They do make good ones and you can get a lighter socket in a 3/4" KO as I recall.
I think I have some older switches lying around that are made for DC as well, I might go check my boxes of junk to find them.
as for the plugs, I do have a few lighter ones, but all of my 12V accessories are wired with 2 wire cords and plugs, but since I am the only one using them, I put a small padlock on the prongs where the holes are so no one else can plug it in.
when I get home later, I will put the inverter on to show you how it is set up, the invertet plugs into the lighter port by the battery, and the yellow cord cap plugs into the inverter (there is no suicide cord)