I haven''t tried this so I'm just talking off the top of my head. The sheds get really fragile as they dry out. More and more with time. I think if I were going to try and keep a book, I would moisten or rehydrate the skin so that it is plyable. I'd then arrange it on a page the way I wanted it, and then press it between stacks of news paper with some added weight (like a stack of books). If you have ever seen a botanist press plant tissue, this is what I am thinking of.
Let it dry completely before you try to do anything with it. It will still be fragile but being flat, you can now close it in a book without smashing it.