Any ideas which 2 colour wires I need to swap over to fix this?
A bit of trial and error, just had to swap the yellow and green wires around. Stick working perfectly now ! 😁
You got lucky this time -- you didn't release the magic smoke that makes all electronics work.

Instead of trial and error, you need to know two things and check the pinout that I linked to earlier -- you
did check the pinouts, right?
1. Is the black wire on the end (Sanwa color order), in the center (Seimitsu color order), or some other color order?
2. Which way are the pins pointing?
- Toward/away from the monitor ==> Sanwa Red + Orange.
- Toward/away from the buttons ==> Sanwa Yellow + Green.

Scott