My first was two weeks overdue, her skin was mostly fine, she was a little wrinkly but not much. The only thing I really noticed (and I think it's a normal baby thing) was she always seemed to have dead skin on her scalp, like it looked like she had severe dandruff.
It never bled or gave her any kind of health or hygiene problem and went away on its own so I didn't think too much of it.
They peel because they have a protective layer over their skin, kind of like a condom so the amniotic fluid doesnt deteriorate their skin and after 41 weeks your body stops pproducing that protective layer. So most likely they will peel.
My baby was five days over due and no wrinkly at all
And sometimes they come out peely when over due. My daughter was 13 days over due and she was super peely but not so much wrinkly.
Ithey don't all come out wrinkly some can yes but my son was 2 weeks late and he was normal and perfectly cute :)