Post a picture of the shad so you gat proper ID by the pros here.
Catch a small BG and use it as bait for the CC. Throw it out there when you are feeding the other fish and see if a CC comes along and nabs your bait. Beware, use heavy enough tackle to make sure it doesn't get away. You have one chance at it. If it get loose, you'll never catch it that way again. And don't expect to catch more than one each time. The others will get spooked fast.
I'm with Dave on the jug-lines, if you can't catch them other ways. Try both BG and the shad as bait, and again make sure everything is good and strong. You don't want them getting away.