Not sure either are very good, probably retaping the flexible is more controllable but not sure how easy that will be to actually do. if you force on to the rod there is a good chance that it will shift to one side as it hits the first part of the thread.

Unfortunately for the kind of precision you need it needs to be turned to ensure it is concentric. I would take John up on his offer and ask for him to turn down a threaded bar with bearings on each end and the last section tuned to 6.35mm so you can use a flexi coupler to the motor.

If its real quick and easy you need then go back to the 10mm and counter bore with 6.35mm and fix to shaft with glue of grubscrew. I have some steppers here that are done the exact same way (except with leadscrews) and they work fine.