Skates and Sharks happily take any fish or squid type bait you drop into the water. The best way to avoid catching them is not to use such baits.
That basically leaves lures, Crustacean and Shellfish. Crabs, Prawns and Crayfish are a good bait to target Rig (which are a shark), While shellfish are good for targeting Moki. For Moki fish near rocks and kelp. The best way to catch Salmon (and Kahawai) without unwanted bi-catch is to lure fish at the river mouths.
For Blue Cod, purchase a boat or take a trip down to the Catlins or Otago Peninsula and fish off the rocky points there. Would also get Butterfish and Moki from the points.