Sigh..here we go again...that troublemaker neutron...sheesh.
The shield will do nothing unless there is radio frequency interference around. But I think you'd notice that.
Power cords can actually affect the sound, but the method for doing this is not one which is typically considered. It has to do with ground loop, how much magnetic field can get in that loop, the loop resistance, and how the loop currents couple within the power amp and source.
It's another one of those "most (including me)" can't hear it, most don't care.
But the high priced ones are not really based in too much fact or engineering.
Lots of floobydust explanations.
Cheers, John