Using the shielded wire from the 68k resistor on the input jack to V1 will reduce the possibility of interference (noise) but you are correct, Fender has gotten away without it (mostly) forever. But they also had issues with oscillation when they “improved” on Leo Fender’s original lead dress in the CBS days. Some of the black face ’60 amps will do it if you dime all the controls (like a Super Reverb for example). Does the oscillation change when you adjust the tone control? As in, roll off the treble?
Ground only one end of the shielding on the shielded cable, it doesn’t matter at which end. On my 2Strokes, I grounded it to the chassis by putting a ground lug on one of the V1 socket screws and soldering it there. Putting a little heat-shrink tubing on the ungrounded end will keep the end of the shielding from touching anything at that end. If you ground both ends of the shielding you will create a ground loop in induce noise rather that prevent it.