As MatzElectronics puts it in this breadboardable joystick listing: “Most breadboard-able joystick modules are overly expensive and too big for smaller breadboards.” This little PSP-1000 — the analog thumbstick from the PlayStation Portable — is small but not too small, and it’s being sold for $5, which solves the other problem nicely. It actually looks quite comfortable to use, so it should make a delightful interface stick.
In addition to the knob itself, the setup comes with an adhesive backing for easy attachment to your next project. It also has four leads soldered on for breadboard use, or it can be used with female jumpers. A bit of solder and heat shrink could also take care of the connections nicely, though perhaps that defeats the point a bit.
The device’s four pins act as two 10K potentiometers, one for the vertical, and one for the horizontal axis of the joystick. This would allow for easy input to an Arduino or the like, or it could certainly be used as a direct interface method for whatever other purpose you might use a pair of 10k pots. For that matter, one could use it as part of a custom video game controller rig, coming full circle with your setup!