Ok. Quick instructions.
Get ultra cheap analog joystick from thrift store. Crack it open, if it has any kind of circuit board, then put it back together and get a different one.
Once you find one that just has wires, buttons, and POTS inside, then you are in business.
Open your paddles, replace the paddle POT and buttons wiring with the POT and wiring from the joystick. One joystick should have two pots and at least 2 buttons, so it should be good for two paddles.