This is my opinion from my experiences in electrical engineering.
Cables are over rated. The cable has a nominal effect on the resistance path to the driver, but at the milivolt range they are being driven at in a set of headphones I don't think it makes much difference at all.
The reason OFC's are popular isn't better audio quality, it's consistent audio quality and longevity. Non OFC's degrade over time as the metal slowly oxidizes. Most of the headphone cables I've seen actually have LESS copper in them when they are OFC than the old variety of braided copper wire.
As for headphones with a connection on only one side: I know people worry about the difference in length causing phase problems, and the difference in material like non OFC metal wire connecting the two halves possibly degrading the signal, I have only this to say.
If you were listening to 2 loudspeakers 100feet away from you and somebody moved one side exactly 8" closer to you, would you be able to tell with your eyes closed? I doubt you could and that is 8" of extra signal path through air, which is a hell of a lot slower than electricity goes through wire, near the speed of light. I can assure you that the difference in length will be completely lost to your listening experience. Our brains are not wired for phase analysis on the femtosecond scale. It's why we can't hear in stereo under water, sound moves faster through water than air, and the sound hitting our left ear arrives much faster than the sound hitting the other ear when it's under water. The brain can't make sense of the miniscule difference in timing, so it appears to hit both at the same time to your perception.
And as for the steel cable introducing some kind of degradation to the signal, you realize that the signal paths inside the components that amplified and decoded the music you're listening to are basically thinly layered foil right? Over the short 8" or so path bridging left to right, there is enough conductor there to carry thousands of times more bandwidth at hundreds of times the voltage without degredation.
So in a nutshell, don't worry about things so much and just try to enjoy the music.