I'll add my $.02 For a little more money you can get better grades of plywood, C-D is general use type stuff that's not too smooth, you can go up to an A-B but it can get expensive but it's also like furniture grade smooth on the A side. I think if you used a good fire resistant sealer and paint on regular plywood you'd be ok because there really isn't that big a risk.
Now that I think about it you could use cheap plywood, line it with thin metal flashing and that would make it sturdy and fire resistant! What do you think about that? You could get a heavy enough flashing pretty cheap, epoxy it to the plywood and you'd be in business. It'd be just like foiling an a/c model (a square one anyway).
I think my last idea made that worth $.03
Eric