The USB joystick internals are different from normal gameport joysticks. In most sticks, the stick movements are still transferred to potmeter movements.
Note: some modern sticks like Microsoft joysticks do not use potmeters, but instead optical encoders. (good for reliability, but unsuitable for hacking).
The joystick potmeters are wired to a small PCB with some electronics on it. Normally one IC (a custom ASIC microcontroller) which deals with the transfer from potmeter resistance to USB to PC game device software.
Still, a potmeter is a potmeter and can easily be replaced by an external potmeter. (The earlier recommendations about jitter still apply)
As you dont need the joystick case, its most convenient to remove the USB PCB from the stick case, together with the USB cable (which provides power and signal).
You should end up with something like the picture above.The connectors at the middle and left are for the potmeters and switches.
With some patience, you can trace the complete circuit connections. It should look something like above.
Note the values on the potmeters (or measure them) In my case they were all 100k, so my external 100k potmeters worked fine with the USB PCB.
I only used axis 1 and 2, so I disconnected the rest, and externally connected the prop pitch and mixture potmeters to the corresponding connector pins. Basically you could also make use of the switches, but for some reason, Flight Unlimited III does not recognize the switches of the second joystick device.
Keep in mind that you need at least one switch to calibrate your joystick, so connecting one external switch is required.
(I would suggest not to solder to the PCB directly. Try to find fitting connectors, and solder the external potmeter (shielded) wires to the wires of the connectors)
Hacking a USB joystick with Force Feedback is described in Adding Force Feedback