Okay, your scale isn't like mine so I can't check it and be sure we will match. Even so, I strongly suspect that screw is a common type.
Suggest you take the scale body/base with you to a good hardware store, Ace/Lowes/H'depot, etc, to their hardware dept. See if you can find a section of threaded rod, brass would be best, that fits. It's probably a number 10 or 12 thread and the rod is usually about 12" long; cut the length you need off that. Round headed "cap nuts" screwed onto each end and secured with a drop of super-glue would provide a bumper on the bottom and a good thumb knob for the top. The same store should have the cap nuts.