Your plan is sound. Yes the prebuilt cables have the shield connected at both ends, due to some US regulation I believe.
Of course floating it at one end is the preferred option if you are re-terminating it.
However - which end should be floated?
Different equipment sounds better with different arrangements.
As a generalization it would seem that to shield a cable from external influences, floating at the IEC end would be best, but if the device radiates any RFI from its power supply, then floating at the wall plug end is best.
However this is just a generalization and different equipment sounds better with one arrangement and not the other. (and despite common practice, many cord/component combinations sound better with shield floated at the wall plug end!)