You are in luck. I was able to get the answer to this question a couple weeks ago after going through the same head scratching you did. The answer is surprisingly simple, and requires no cutting, crimping, soldering or anything. Just unplug and plug.
You do not need the wires that come attached to the Happs trackball. I originally thought you needed them in order to wire up to the Minipac, but they're for a different type of interface -- probably a more arcade-authentic one. You can unplug this harness that came with the unit and put the wiring away in case a need for it ever arises at a future time. The wiring harness supplied by Andy for the Minipac has four molex connectors, I believe. Two of them are the same size and look and will attach to the pins on the circuit board of the trackball (use the diagram to determine which goes to the x axis and which goes to the y axis); another molex is a beige one that would connect to the circuit board of a spinner, and the remaining black molex needs to attach to the Minipac.
That's all it takes. If you have any questions with the Minipac and wiring it up feel free to ask.