You should use bait elastic with prawns and crabs, I use a lot with crabs in particular. Cotton is probably better than nothing if you’re not near a fishing shop.
Never tried cooked crabs, I suspect they wouldn’t work as well as raw crabs because the scent wouldn’t be as strong and would be different from what the fish are familiar with.. although I’ve caught a variety of different species on cooked prawns. If you’re using two hooks with two baits, put the crab on the bottom hook. I don’t remember ever catching a dogfish on crab but they will occasionally go for prawns (nowhere near as much as they’ll go for squid).
I think I’ll go to either Taumutu or Bayleys beach tomorrow night, hopefully there will be something around.