I think you mean 1/2" thickness and the lumber would be called figured. The great cabinetmakers of the past didn't have a band saw, a table saw or electricity. Pieces that small could easily be cut with a handsaw and a little elbow grease, then hand planed or sanded. Don't let lack of a tool hold you back.
There are tons of wood suppliers on line, even Ebay with select small pieces for sale. Some will do custom milling and a variety may be available near you at different woodworking suppliers. Google up figured lumber and the choices are astounding.