It's in the gray part of the cable though, BEFORE the strain relief. If I cut it and solder, 1., the cord will be a few inches shorter, and 2., there will be no strain relief, and will look kind of hacked/odd. Was hoping there was some sort of cable I could swap it out with.
Edit: looked at one closer. Almost looks like the strain relief is not part of the cable, and might be able to be moved. I'll look closer tomorrow.