The NZ Teaching Council aren't part of the same organization as NZQA and INZ, so their requirements can be different.
I see it says here
https://teachingcouncil.nz/content/overseas-teachers that they require certified copies of documents. I suggest, then, that you can ask someone in Spain to get your originals copied and certified, and send those certified copies to you by post, or send the originals for your to have copied and certified (NZ JPs don't charge for that service). Also, your translator can be asked to print off and sign the translations.