Hi Tich,
Below is my thoughts but I suggest getting expert advice:
Immigration may assess if you can afford to get speech therapy for your son here in NZ if not already covered for him in the school you decide to send him to.
However if you do apply for Residency after working here for the required period of time, Immigration will check if your son's hearing condition will be more costly to the NZ Public health system than the limit allowed at the time. Since your son already has 2 cochlear implants - he should meet the criteria and you may not even need a medical waiver. However, as with what happened with my application, you may have to take your son to get a letter from an ENT specialist here in New Zealand if they ask you to.
Cheers, Sim1602