I don't understand your question. Are you are talking about cutting off the plug on the output (low voltage) side? If so, the output wire is usually only two conductors; sometimes a flat "zip" cord, sometimes a coaxial (center conductor and shield) cable.
It doesn't matter which type of wire comes out. You will have to experimentally determine which of the the two conductors is positive and which is negative; there seems to be no consistency. The wire with the white tracer might be either neg or pos. The center conductor might be pos or neg.
In all the wall-wart transformers I have looked at, neither of the output wires is common to the transformer input, even if the line side has a three prong line cord. That is not the case if the brick is actually a switch-mode electronic power supply (not a heavy transformer). You can usually tell just by the weight if you have a real transformer or an SMPS.