I've heard that the American shad in the Del. River will not bite until they migrate up to the vicinity of Easton, PA. From there they are caught all the way up to New York, but I've never heard of shad caught in northern Delaware.
Many years ago I caught white shad below the dam on the Brandywine in Wilmington. Have not been back to that area in long, long time. Might be worth a look. You could see them from the Market St. bridge.