Whatever shorts that you are comfy riding in, they dont need to be cycle specific unless your doing some major milage where confort is an issue. To my knowledge, all road specific shorts will be lycra (or tight), makes sense for aerodynamics, why ride an aerodynamic bike then slow it down with baggy clothes causing drag.
I pootle about wearing anything from camo shorts to denim shorts, no issues whatsoever(never done anything really long distance yet). No cycle specific clothing.
You could always buy padded undershorts and wear them under whatever shorts you like to wear for comfort without feeling self concious wearing lycra if it bothers you.