Sorry, guess I wasn't clear. Here's another shot:
The Crack output impedance, as I said, is 100-150 ohms. Headphones are rated for impedance, usually, between 30 and 600 ohms. If you are using 500 ohm headphones, then they are higher than 100-150 ohms and the outer foil should go to the amp side. If you have 30 ohms phones, then it would go to the headphone side. If the phones are 120 ohms, it shouldn't make any difference. In practice, I doubt it would make a noticeable difference no matter what phones you have, since all these impedance are quite low relative to the reactance of capacitive coupling between the cap and anything else in the circuit.
Of course, lots of unexpected things turn out to be audible. There is only one way to tell, and that's to try it yourself. Because of the DC voltage being blocked by the capacitor, it would be wise to give the cap a hundred hours or so of music after reversing it, to see if there is a break-in effect which needs to be reversed along with the capacitor.