I have travelled on an NZ 737 once with a carry on guitar [long story - suffice to say I have no idea how to play a guitar], this would have been a few years back now.
At Check in they tagged it to my destination but told me I could take it with me to the gate. So I took it through security (no problems there) and I just boarded and put it in the overhead locker. No problem.
With NZ the only thing I have ever had to check-in that I didn't want to was a snowboard (And even then it probably was a good idea). If you have a legit reason to carry something on, in my experience they aren't likely to stop you - as examples I have carried on very hastly wrapped Royal Doulton stemware, oil paintings, a huge bunch of flowers, and once even a very large polish glass vase.
I also once remember turning up to check-in at AKL with a big bulky computer monitor. We taped a piece of card over the glass, put it in a plastic bag and sent it on its way (after signing the necessary liability waiver of course!).
Easy.