It's very light & inexpensive plywood. Home Depot sells it in 2'x2' squares, I'd use 3/32". Take out your insoles, trace it on the plywood and cut. Put the wood insoles in first then replace the shoe's original insole. Should stiffen things up a bit.

Here's a link for cedar veneer insoles. the Luan would be a bit thicker and stiffer but the same principle. http://www.furnier.de/Pressemeldung....708c95c6fa4858