It wont fit, strangely...and that vinyl is there for a reason, best not to tamper with that.
I do not know where you got your Xbox PSU (its really a GFCI, not a PSU), but all the ones I have, look like a proper PC power cable should fit, but the ground pin is missing on the female side. Its best to track down a proper one. Basically, the official coard is wired in such a way, where the ground pin is used, if you tried to use a PC one, you would not have the benefits of ground, and your 360 GFCI will be prone to shorts and maybe fire in a surge.