I wouldn't recommend attempting to shorten the cable of a circular needle. I've seen it done before, by cutting the cable and re-attaching it with duct tape! But it wasn't pretty! It was functional, because the needles were large like yours, so the stitches were big enough that they were able to slide over the thick tape reasonably well. I guess it's doable, but as an experienced knitter, I think of that as ruining a great set of needles that you'll one day want for another project! My own solution would be to...
1) Buy or borrow a pair of 16" circulars, or
2) Knit it flat (back and forth) with those needles, and seam it up the back.
3) Buy or borrow a second set of 8mm circulars (of any length), and do the two-circular needle method, using both needles.
4) Use whatever I could get my hands on; DPN's would also work of course.
That cable might
not long enough to do a hat with Magic Loop method, as others were suggesting. It probably would be long enough, but I'm not sure. You can do really tiny knitting with a 24", but a hat has a lot more stitches. I'm not that experienced with ML, so I'd be curious to hear if that needle does work if you try it!
Of course, if you're all pumped up to cut this circular needle, and that's where you're at, then go for it! I've done similar things, and it's fun to break the rules. LOL.