Quite a bit to cover here.
The south Island offers two different ‘groups’ of fishing. In Nelson and the Marlborough sounds the main target species include Snapper and Kingfish. Most people fish dead bait for Snapper, and live bait for Kingfish. Could be worth a few days exploring around the Marlborough Sounds, Tasman Bay, Golden Bay and even around to the wilds of Westhaven inlet and further south. The size of the Kahawai (Australian Salmon) which can be caught off the river mouths of South of West haven are impressive.
Further south Shark species start to dominate, bait anglers often target Rig/Lemon Fish which is a cousin to your gummy shark. Paddle crab is the best bait but it is hard to purchase. Other sharks include moderate size (up to 100lb) Sevengiller and Tope. The occasional Skate, Ray, Conger would also get caught.
Kahawai can be caught almost anywhere, they are common around river mouths and would readily be caught on most styles of fishing. When you get Further south then Marlborough you enter “Salmon country”, from my understanding Salmon fishing involves spinning at river mouths all day for many days and you might get to see someone catch a Salmon. I have heard that F&G rangers would pester anglers targeting Kahawai (They claim that they are targeting Salmon) if they do not have a freshwater License. There is no license required for catching any saltwater species.
Blue Moki is another species which can be easily caught. They are often caught on shrimp, mussel baits and feed best at night.
Towns / places to visit.
Kaikoura is worth a look. Fishing off the wharfs at night can catch good numbers of Blue Moki. During the day there is plenty of surf beaches to chase sharks (but in my experinece the surf fishing is slow around Kaikoura proper). There is also many rivers which enter the sea which would provide good opportunity for spinning.
About 30-40 minutes to the north is a good series of Surf Beaches which regularly produce decent size sharks over high tide.
Blenheim offers decent river mouth fishing for Kahawai (Wairau and Diversion) but I probably would not spend any time there for the fishing. I would advise to head into the Sounds and aim for either French pass or Titirangi (or both). There is camping offered at both locations. French Pass would be the more scenic of the two and would offer the best chance to catch a Kingfish. Snapper, Gurnard, Blue Cod and Kahawai can also be caught.
Its a little out of the way but it could be interesting to explore Golden Bay and around to North-west Nelson (west-haven and further south). Snapper and large river mouth Kahawai would be the target species there.
Then its a long drive back down around to the Westcoast. River mouth fishing for Kahawai/trout is a option down the coast. All kinds of species can be caught in the surf on bait. Karamea to the north is cool but you probably would not have time. The next fishing highlight would be all the way down in Haast. Down there you would be fishing cooler waters and the Kahwai would be uncommon. Never fished it myself but certain something worth catching would be about.
Then I would head over and down to Stewart Island, the fishing around Stewart is a bit less spoiled and you should get onto Blue Cod (excellent eating) and good size moki. Trumpeter might also be around.
From my understanding the fishing up the coast towards Christchurch is a bit ‘average’. You would catch Sharks, moki and a few other species. The further north you get the Kahawai would return to the river mouths.
Freshwater fishing for trout is also plentiful.
Not many poisonous fish in our waters, if you do bait fishing you are likely to catch a Spiny Dogfish which has a single spike which normally causes a infection if you get stabbed by it. Rays also have tail stings but with care they can be avoided.