Consider the device. If it has an IEC outlet, it should pass FCC emissions standards with ANY cord attached! That’s the facts. But, if you want to be careful consider what the component is. If it is a digital device, like Paul says, they are prone to being noisey. They are what cause the problems, not the ingress from the outside world. FCC looks at INGRESS and EGRESS, both. YOU may be the problem!
You may consider a shielded power cord on THOSE noisey devices. A pure analog device not so much.
Shields alter the ground plane reference values over distance. This makes a cables electricals values irregular based on the presision of the grounds physical proximity to the core wires. UTP cable are “shielded” but they are shielded to the reference world outside the cable core, that’s the earth as it may be. The true E field is stopped by the inner surface of the shield until the E field turns into a B field at very low frequencies. The B and E fields magnitude switch places as frequency drops. At RF, the E field inner shield distance determines the cables “impedance” across frequency by altering the capacitance.
A shield creates another version of earth but one that is far, far closer to the cable. We can determine what this earth is, and manipulate it to alter cable electrials (shield, wire and core size etc on a coaxial cable).
Since the core is so CLOSE, the effects of physically moving it is very pronounced. It is imparative at RF to manage the shields physical distance over length or it is actually WORST than no shield at all. This is why shields are best when it is verified that one is needed. An Unshielded Ethernet cable has a far better internal electrical NEXT, Near End Cross Talk, and ACR, Attenuation to Crosstalk Ratio, than the shielded version. Internal cross talk is 6 dB better on the UTP cable. A shield creates inductive coupling of the internally captured EM fields. UTP is also has a more stable electrical impedance cross frequency. This improves RL, Return Loss reflection, off a load at RF.
Why use a shield? Easy, when the noise coming in alters the signal to noise ratio MORE than the negative effects of using a shield. If I have noise below that threshold, it is better to use a UTP cable. If the cross talk is 6 dB worse with shield (it is), but ingress noise makes it 12 dB worse, a shield adds 6 dB of cross talk margin than a UTP, for instance.
The lower you go in frequency the less the shields physical perfection matters as the EM wave ignores the shield! Yes folks, a shield won’t stop low frequency noise. Only a low permeability path (a magnet will stick to it) shields the noise we see around motors and AC high current lines. Here we use passive cancellation (XLR type designs) as the most practical method to remove what we don’t and keep what we do. The next cheapest thing to do is DISTANCE as EM fields drop with distance squared.
Sure, you can put your cables into low permeability conduit and get the best of E and B field shielding. Just make sure you are good at tube bending!