Hi,
i have an unusual but simple approach for you. You could attach 2 normal RC servos to Arduino (using the servo library; don't forget to power the Servos externally and not with the 5V from Arduino!). Then use the servos to drive the joysticks on your transmitter. This was you don't even need to open the transmitter and - if you fit them removable - won't even lose garanty...The main advantage is that you don't need to hamper with the correct values of digitals potentiometers and how to fit in your concrete transmitter. Ok, it's not so elegant, but who cares...
Best regards Mekanax