Remove the old wires from the driver and use new wires.
Soldering the wires on the pcb first makes it a lot easier to get clean, low profile joints on the pcb. This helps minimize problems with not having enough room to clear the reflector. It makes it tougher to get clean joints on the driver, but those joints don’t have to be as clean.
Also, it’s how Dr. Jones does it, and many other experienced builders do it that way too.
You’re right, but those would have to be some extremely low solder joints and extremely flat wires.