It looks like the wire that goes from the fuse to the 5Y3 socket connects to the 0.01uF ceramic cap, the other side of the cap goes to the chassis. The terminal on the 5Y3 socket is just used as tie point, it does not connect to the 5Y3. This is the so called "Death Cap". The cap and wire should be removed, you don't need it with a three wire line cord. Current safety standards connect the fuse and switch on the hot side of the line, the black wire in the line cord. The white or neutral wire form the liine cord should go straight to the transformer. The green wire from the line cord should attach to the chassis with it's own screw, nut and lock washer not used for any other purpose.
Edit: The switch being on the volume control will tend to inject hum into the audio. Keep the switch wires as far from the pot wires as you can. You may have to install shielded wires to the pot or install a separate switch to lower the hum.