Babies don't feel it, so don't worry that it's hurting them. My DS liked grabbing and pulling at things, which during a diaper change meant his cord clamp. It ended up getting pulled off almost completely at 3 days old, and fell off completely at 5 or 6. We just kept the area clean and dry. We did put a bandaid over it for a bit, so his clothes wouldn't stick to it, but the bandaid ended up sticking. He never cried b/c of us cleaning it or the bandaid or clothes getting stuck to some of the gunk. Just keep it clean, put a bit of breastmilk on it and let it dry. It'll be fine if you clip it off.