First, its important to note that the Glowforge was not designed to be serviced in any reasonable manner.
That being said, the HV wire (red) cannot be removed from the power supply without compromising the insulation. The only non-destructive way to remove the supply with this lead intact is to disconnect it from the tube, and pull it all the way out through the long path they threaded it through (it’s about 5 feet long, if I recall correctly).
I attach a pull string to it so I can easily thread it back through upon reassembly.
The return wire (white) can be cut near the supply and soldered back together when you reassemble it. If you take this route, be sure to insulate the soldered joint with heatshrink or something similiar. You could also unfolded the wire from the ballast resistor on the left side of the chassis (that’s what I do).
All around, removal and reinstallation the power supply is huge pain in the ass.