I just looked at his vid. I note the correctly sized arbor to remove any radial displacement. I note his glue is at the periphery, where it will set and there is a finite glue thickness. I also note that all cuts were made such that the item could not fly off and go into orbit without breaking the arbor. That is except the final chamfer on the back side of the flywheel outer edge.
Seems safe enough. Light cuts with a sharp tool and keep out of the line of fire, should anything go wrong (it can happen). An appropriate anaerobic loctite, and leave for long enough to cure, might be another/better alternative to pound shop glue.
If you are still overly hysterical, then use a longer arbor and thread it for a holding nut? Drill through (where one or more of the final holes were going to be positioned) into the holding mandrel, thread and screw in some brass threaded rod. Lots of ways to go OTT on the safety aspect, if you are that worried, I am sure!