Ponta Delgada could refer to anywhere in the council of Ponta Delgada (like a county in America) or the city of Ponta Delgada itself. Everything in the Azores is organized on the town level, so you need to know the exact town.
1917 is too recent for online records. You might be able to find the baptism of Brazelina, but it's a needle-in-the-haystack method. I'd start with the 3 churches in Ponta Delgada, making note of every Brazelina that you find. Then I'd do all the other 17 parishes in Ponta Delgada. You will be able to eliminate a couple of Brazelina's based on age. And you have have only a couple left to pick from. Then you'd need to find her marriage. If she married between 1910 and 1917 though, you're out of luck, as the online records for parts of Ponta Delgada end in 1910 (and some end earlier).
Here's the link for the online records. If you need to navigate in English, click the British flag in the upper right corner.
The Passaportes OUT of the Azores are online for the port of Ponta Delgada and go up to 1939. If you know when they got to New Zealand, you might be able to narrow it down. Scroll down to the port of Ponta Delgada:
https://tombo.pt/d/acores
I think you need to do more research in New Zealand to help narrow your search. We have a few researchers who have experience with NZ who may be able to help.
Also, DNA may help.
Cheri Mello
Listowner, Azores-Gen
Researching: São Miguel island: Vila Franca, Ponta Garca, Ribeira Quente, Ribeira das Tainhas, Achada