Hi fellow Wellingtonians, I came from a similar background, sailing P Class off Eastbourne beach as a kid.
Cook St isn’t that bad, don’t let it dictate the boat
you buy. Any well kept keeler will get across safely on a good day, and on a bad day any boat will struggle. The trick is only to cross on good days.
We’ve had a Lotus 950 and now have a Jeanneau
43DS, both handle the Strait easily. The Jeanneau
even handles it on a bad day (yes I broke my rule
and crossed when I should have known better).
So find something you will enjoy sailing and can afford, rather than an icebreaker to handle the Strait on a bad day.