I used surfing booties a lot in the past - they’re like dive boots but with a supple sole. Just like anything made to go in the ocean the more you spend the better quality you get, but some reasonable options can be had for $60 if you want to try them out. Buy 5mm if you’re wanting warmer, but 3mm should be enough for north island.
Something like this or similar
https://www.hydrosurf.co.nz/wetsuits.../ewp2749m.aspx
The more expensive ones will be warmer and softer and easier to put on. They’re epic for river crossings as you’d imagine.
I’ve been using the vivomove brand ones from Australia now for a couple years and can confirm they are the ducks nuts! They are expensive but so so good, you can feel the ground and flex the sole but also get good ankle support etc. if you’re buying on a budget they do come out with a couple sales a year - check them out
https://vivobarefoot.com.au/collecti...42705087103193