I would stick with a fat bunker chunk, cut off the tail and head. You can definitely chum off the beach. I'd go to the local fish store and get whatever scraps you can and chunk/chum them off the beach. I used to bring a 2x4 to smash the mussels along the jetty to attract black fish and sea bass. I always chuck my "clam parts" in the ocean when I'm bassin.
Just don't start chummin between the swimming flags and you'll be fine.
Good luck! Those brown sharks are out there and they are fun to catch and release!