I didn't try it with Duelund cables but I DIY speaker cables with similar construction and providing a shield improvement the sound quality (mostly blackness and image). The shield having equivalent gauge is used as the ground lead. The added capacitance will provide a path to ground for high frequency noise. Give it a try to see if you like it.
A shield can keep RF out, but whether it affects the sound is unknown.
But the extra capacitance would form a filter to diminish the higher notes.
One sort of needs some proof as to which is happening to assign a root cause to the effect.
And it is unclear whether the effect is real.
In any case I am assuming that the shield is floated at the amp and speaker, and tied directly to some ground like the safety ground?
And the other good news in that the cotton would make the addition of a shield have a lower capacitance than it wold have with a higher dielectric constant material. So the cotton coming in lower.