Janie, my very Southern mother and father preferred the cabbage sliced very thin by hand by my patient father! One can sparingly use a bit of sour cream or thick yoghurt in combination with mayonaise, honey and vinegar to achieve the desired balance of sweet/sour/creamy/crisp.
I have enjoyed very thin-cut, crisp and sweet (not sweetened) cabbage in slaw with drained crushed pineapple mixed in with the vinegar and mayonnaise. I was surprised it was so good.