You could get a raspberry pi and a camera module. MotionEye can be installed as the OS. It requires a network connection to your LAN to set it up, but it can be disconnected afterwards. I believe it can be configured to store all files locally.
Edit: Fixed link
I’m still trying to wrap my head around fingerprinting, so excuse my ignorance. Doesn’t an installed plugin such as Canvas Blocker make you more uniquely identifiable? My reasoning is that very few people have this plugin relatively speaking.