Wood core would be perfect, either birch or balsa. Birch core is probably stronger. Don’t worry thinking the wood will add weight, it won’t add but a few ounces of weight.
Try this lay up if you have some carbon fiber cloth:
colored kevlar/carbon fiber/ core/ carbon fiber/colored kevlar.
I mentioned colored kevlar because your wink mirror is hybrid colored cloth. Just assuming this is what you would be using.
The edges of the core that show when cut you can lay down some resin coats on the edges and tint the resin black or whatever color using resin dye.
We have a bunch of these to make for a customer in the next couple weeks. I’m going to lay up one large flat panel then cut the pieces out. It will take some time epoxing the edges and sanding them smooth.