Speaking of dehydration, it is possible to dry out a piece of orange peel. If you do it properly so it does not rot or get moldy, it will last for years, although it will gradually use its aroma. The problem is that it will shrink when dehydrating, resulting in a worse-looking surface and possibly distorting the signature. A largish section is also practically impossible to flatten, so you will have to live with a curled piece-of-sphere shape. The end product is very stiff and somewhat brittle, with irregular surface whose color is a darkened, somewhat dirty looking orange, not the bright hue of the fresh peel.
You can find instructions for drying orange peel for use in teas or as ground spice. The way we used to do it at my parent's home was to put a single layer of peel pieces on a high shelf and let them sit there for a few weeks. This will not work if your climate is humid, so you might prefer a method using a dehydrator or a low oven.
This site has not only instructions, but also a good picture of the end result. They remove most of the pith (the white part) to prevent bitterness, but in your case, it is preferable to leave 3-4 mm to ensure structural integrity. You can leave all of it if it is a thin-peel variety, but remove some if it is very thick, because you risk rotting and bad texture and geometry.