Some of the speeds that people are quoting are getting pretty scary. Also, there was a technique quoted about wrapping a flywheel with safety wire to keep it intact. While I’m sure this works reasonably well, it does seem to be pushing boundaries of safety when you are relying on a secondary method like this to keep things intact.
The basic analysis for hoop stress is easy too look up and relatively straight-forward to calculate for simple rings and simple cylindrical disks. You will probably find that the material, in theory, has a decent safety margin. The problem is really how well do you trust the manufacturing of the parts. If you are dealing with a metal wheel, you can probably be reasonably satisfied that the material is decent quality without defects, but other types of wheels like plastic molded wheels may not be as high of quality. Small defects can significantly reduce the strength of the material relative to it’s theoretical strength.
There are ways to assure yourself of the safety of the system. A test to something like 120% or more of the maximum speed would provide adequate assurance of the strength of the wheel. Obviously, that test would be done in a safe enclosure of some kind that would protect personnel from any failures. 120% overspeed testing is the standard that is used for jet engine rotors.
As far as balancing the rotor. This is obviously important. Most of the wheels that are commercially available would have a decent balance. But if you are joining things together in assembly, then this can be a problem. It is also relatively easy to test and doesn’t require high speeds or dangerous setups. Mounting the wheel on a reasonably lightweight structure, any imbalance, even at lower speeds, will result in tactile vibrations. Correcting it is another matter. It is possible to balance wheels, but you need some fairly sophisticated balancing equipment to do so. The best bet would be to build your wheel assemblies carefully making sure that you keep things concentric and co-axial as you go.
I agree with you, it is a little scary. So please be careful.