That's the problem! Shielded audio cable is good for eliminating electrostatic interference, which is a common cause of audio noise. But, it does practically NOTHING to eliminate low-frequency magnetic (inductive) interference. And, a computer monitor is exactly a source of magnetic radiation at several frequencies. The horizontal sweep and the switching power supply frequencies can be shielded to some extent, but it is not really practical. The vertical sweep (50 - 100 Hz) can't be shielded without insane effort, so the only real way out is to eliminate its influence on the circuit. That's why professional audio types use balanced circuits for mikes and all sorts of other low-level signals.
in the presence of interference sources, clearly NOT true!
Forget this diameter stuff. Unless the cables were FEET in diameter, and almost all solid copper, they'd have NO effect on 60 Hz magnetic fields. These fields penetrate conductors.
If you can route long cables away from the source (the CRT is by FAR the worst offender) that is the simplest approach. If not, a pair of transformers and a balanced, shielded cable should also work. But, the TRANSFORMERS need to be shielded! Many cheap audio transformers are NOT magnetically shielded, just put in a pot-metal box. if they are near any power transformers or CRTs, they can make the problem WORSE! If you think a single wire stretched in space can pick up a signal, how bad would 10,000 turns of wire be?
Jon