I guess you'd basically be turning them into bongo cajon hybrid. In a cajon you use a very thin plywood [I used something called doorskin. A vey thin ply used in cheap doors and can be bought in quarter sheets].
If you didn't glue you could try a couple materials ... why not a plastic even?
1/8 inch baltic birch pylwood very stable, no splitting, warping or shrinking issues. because there's no voids or knots in the interior plys's you get a very sharp clean sound. Its mainly sold to cabinet shops not that readily available to the public. I have a couple of pieces that would fit your needs. you can have them if your willing to pay for shipping. I live in canada.