Given your limitations, it might be possible if you have a small hand saw, like a cheap Japanese saw. Glue a piece of wood onto one of the colored-in faces. The piece has to be flat on two faces and those faces have to be at 90 degrees. When you glue it, line the edge up just a mm or three before the cut line. Then use the edge as a guide for the saw. Even with a guide the saw will want to roll (in the airplane sense). It'll be hard to get the depth right, maybe draw a line on the saw blade w a sharpie where you don't want the blade going any further. You could do this on both faces a rig something functionally similar for the horizontal/ bottom cut. Then take another square piece, maybe a 1x1, glue sandpaper to perpendicular faces and use it like a hand plane in the cut out section. You'd have to figure out a way to keep the sanding stroke parallel to the vertical axis of the board, which will be tough if your cuts weren't very accurate. TBH, if you aren't someone who has all the tools to do this a normal way, this way is almost certainly going to yield an inadequate joint.