Can you get a wire in between the flyback coil and core ? If so you just make your own winding that is totally floating. Start with one turn and work your way up until the filament is bright enough.

It is better if you have measuring equipment. A true RMS meter can read the waveform at 6.3 volts RMS but not everyone has that. A scope should show about 20 volts peak to peak, that corresponds to about 6.3 volts RMS with that waveform which is usually a half sine resonated at 5 times the horizontal sweep frequency. Iff the monitor has fast retrace it might have to be a bit higher. In any case, use as little as possible to get a decent display. The less the better as it will result in the longest cathode life. The cathode has already been abused putting out more current than was ever intended..

They used to make a small cathode transformer for insulation but finding one today rather than a piece of wire is not easy.

If you can't get in between that core and coil on the flyback get back to us and I will see if I can think of another solution.