Is it cruel to shave a cat?

One of my kitties has something sticky in her fur, matting it. I have no clue what it is or where it came from. I’ve tried a bath (seemed worse after that), tons of brushing, and have even cut some of it out with scissors, but can’t seem to get all of it. Whatever it is, it’s in a few different spots on her back. It doesn’t seem to bother her much, but it bothers me. She’s a wonderfully silky feeling cat, until your hand hits those “speed bumps”. Not only are the spots matted, they feel kind of… waxy.

My next idea is to groom her down to nothing, at least in those areas. Is it be better to shave all of her fur or just those areas? Would that cause her distress? If so, what other ideas would you suggest?