Cut some 1/8" teak flitches and epoxy a layer of 6 oz glass cloth to one side. Assemble the box with cyanoacyrlate glue then glass the outside with epoxy. Fill the weave on of the glass with epoxy then varnish. It will look like 1/8" teak, but will be plenty strong. In fact you could go as thin as 1/16" for the teak and still have it adequately strong.