American style joysticks are rather simple in design, can it be reverse engineered and 3D printed? Yes.
I added some features like interchangeable restrictor plates (4-way or 8-way) and varying sized actuators to customize the feel. In the end I made a working tactile switch joystick at 50% scale for about $3.40 in parts and filament.
Printed on a PrintrBot Simple Metal
Layer Height 0.25mm
Shell thickness 0.8mm
Fill Density 20% for large parts, 50% on small parts
Print Speed 60 mm/s @208 C
Hatchbox PLA filament 1.75mm dia