I wouldn't recommend unpadded shorts even if I knew of their existence. Get some lycra cycling shorts and be comfortable. Cycling jerseys have 3 big pockets in the back that are far better at carrying stuff than shorts pockets, another thing I wouldn't recommend.

If you insist on continuing your masochistic riding ways, go to Dick's Sporting goods and buy whatever strikes your fancy; but avoid cotton and look for stuff with no seams in the crotch.