You can use the pre-shredded cole slaw veggie bags at the grocery store if you wish (broccoli slaw bags also work). I do that at home sometimes, but the cabbage is more likely to wilt or brown if it is pre-shredded and you are waiting a few days to actually use it, plus it makes it less home-made and therefore braggable.
If camping, I pre-dice the onions and peppers at home and put in a small zip-lock bag, and pre-boil/mix the liquid ingredients and put in a jar or tupperware container, and re-warm it before tossing with the cabbage. This leaves only the cabbage and carrots to prep in camp.
You can skip the carrots or the peppers or the onion if you wish, but you probably shouldn’t skip the cabbage–unless you’re doing broccoli slaw, of course…