I would definitely get in touch with NZIS first.
However don't assume that it means you can't go, as mother bear said they are only concerned that you won't cost them much in health care.
The criteria is that you will not cost them more than $15K in the first four years. If he is now fit and healthy and not likely to need much in the way of treatment for a long time to come, you could be OK

If you apply you will most likely get an initial recommendation for rejection. Your application will then be referred over to the chief medical assessor in NZ, if he also recommends rejection you will then have the opportunity to give more information. If that fails, you can then appeal, if that fails you will then be entitle to apply for a medical waiver.

However, if when you submit your application form, you give all the information, including consultants reports, you may be able to be accepted without going through all that hassle. ie. Do not just submit the medical report on its own.