Nope, should be good to go. I get what you mean, it took me a while to realize what C120 was as well. I eventually learned about it years ago when I think someone like Poweraddicts took his apart or something.
It might be difficult to take the box apart to remove the ground, you might be better off just leaving both of them fastened to the alternator and put the new cable on top and run it to the engine block. In all honesty, your stock ground is likely still fine so unless you just really want to use the cables you bought, you probably don't need to and won't benefit from changing that one out.