One of the challenges with the really small cameras is picture quality. I have one of the endoscope type cameras for looking inside boilers and while it is good enough to have a look at the internal surfaces and the silver soldering the quality of the picture is pretty grim. That connects to my laptop and I would have to do a screen capture from the live feed to get a picture. You might get a better picture with really good lighting and they are really cheap so you can have fun playing with them. They might have improved a lot since i bought mine as well.
I have recently been playing around with one of the small cube type Go-Pro cameras and again for video not brilliant pictures but they can also be used for single pictures and can be operated remotely by a control unit, available separately, or via an app on your smart phone. I haven't done this but it might be what you are looking for. The type of Go-Pro you want is the Go-Pro Hero Session. No longer made but available second hand and in good condition if you search. They measure up at around 3.5cm cube so about the smallest reasonable quality camera out there.