You don't need to discharge the tube (unless you cant replace the fuse without removing the chassis+anode wire, which then of course you need to discharge the tube) but you certainly better check to see if the large filter capacitors on the chassis still have a charge (typical if a fuse is blown and it has recently been plugged in to test.
The simple test it to take a multi-meter and test both sides of the fuse when set on 200 VAC. Is there any voltage across the blown fuse? If so, you can bet there is a charged capacitor somewhere. If not, then double check voltages across the larger capacitors, and if not, then it's safe to work to desolder and replace the fuse.