They are indeed potentiometers and not optical like most spinners.
The cheap part is the hard part, because a potentiometer of high enough quality to use in a paddle controller will run 15-20 euros each. That cost keep shoving the restoration of my 4 player William's Pro Tennis (Pong) to the back of the line because I don't want to drop $100 on rebuilding the paddles when it will probably won't even see another 50 plays over the next 20 years.