It's unlikely that shortest is best for power cords.
Most power cords (PCs) passively filter high frequency noise (e.g., in the kHz to MHz range) by acting as a distributed capacitor. Here's how it works:
A capacitor acts as a high pass filter. The text book equation for capacitance's role in impedance (resistance to AC) is: Xc = 1 / (2*pi*f*C). Notice that both the frequency (f) and the amount of capacitance (C) are in the denominator, so as the product increases (i.e., more capacitance or a higher frequency), then there is less of a resistance (strictly: impedance) to those frequency components of the wave. 'pi' is the constant 3.14159… . So if you would put a capacitor between the hot and neutral lines, high frequencies would "short" across, but low frequencies (e.g., the 60 Hz fundamental wave) would be left intact. This is the mechanism behind the "Auricap tweak".
In PCs, various geometries (e.g., twisted pairs) and dielectrics (i.e., the type and thickness of the insulation on the individuals wires) are used to establish the cable's capacitance. By bringing the hot and neutral into close physical contact, capacitance is created between them. High frequency noise on the hot wire will "short" across the insulation to the neutral (and of course vice-versa; remember in AC, the "hot" has a voltage [potential], but both wires carry current). The "short" doesn't cause a problem because the voltage and current at those frequencies are so low that the excess energy is easily and safely dissipated as heat.
Clearly, the tighter the hot and neutral wires are twisted in close contact, or the thinner the insulation, or **the longer the length of contact**, the higher the total capacitance. So if you replace a 2 m cable w/ one that is only 1 m, you've cut the capacitance--and the cable's ability to filter--in half.
Does that mean longer is better? Not necessarily. If the cable is too long, you may need to wrap it upon itself--raising the inductance and reducing the capacitance--or it may fall near other PCs--creating electromagnetic interference on both cables. But it certainly means that there really can be a notion of "too short". "Too short" is that length such that the cable's capacitance is insufficient to adequately filter the high frequency noise on your line.
Maybe "more capacitance" isn't right for your system--though it is hard to see how on a PC it could harm the sound. Basically, even with clean power, extra PC capacitance should simply result in no observable effect, because if there is nothing to filter in the kHz and MHz range, it shouldn't effect the 60 Hz wave. Note: this also means that that PCs--and really all passive power filters--can really do nothing about low frequency harmonics; for that you need active filtering. So you cannot achieve totally clean power with only passive devices unless your power already has no low frequency harmonics (unlikely).
For speaker cables, we are not interested in filtering a 60 Hz fundamental, but rather in preserving 20 Hz – 20 kHz range given "modest" voltage and current capacities; for interconnects, the frequency range is the same as for a speaker cable, but the current is far lower than the voltage, so capacitance is a real issue (read: bad). So all three cable applications require notably different considerations.