After swimming for a while, Mrs Patuwai-Parker said she saw the captain motoring the boat to a new location in deeper water on the other side of coral reefs, about 40m from them.
The couple started feeling tired and Mr Parker, who was diabetic, said he was feeling low in sugar.
Mrs Patuwai-Parker started waving to the boat and calling for help as she started going under the water.
An Italian couple swam over to help her while Mr Parker, who "seemed to be tired-looking but okay" swam towards the boat on his back.
Auckland couple Hannah Goodburn and James Rennie went to help Mr Parker when he put his hand up, signalling he was in trouble.
They held his arms and tried to keep his head above the waves while they yelled for the boat to hurry up.
"The boat was still ages away and didn't appear to be attempting to come to us at all," Ms Goodburn said.
"Suddenly, I noticed that Graeme's face had gone purple. I also think his body had sunk into the water and only his head was above water."
Mr Rennie attempted CPR in the water while they waited five to seven minutes for the boat to arrive.
Mr Rennie and a German doctor who happened to be on board continued CPR when they made it onto the boat.
They were advised that there was no medical equipment, specifically a defibrillator or medical kit, onboard.
Mr Parker was taken to an ambulance waiting on shore - which also had no defibrillator or other important equipment available - and he was pronounced dead 10 minutes after arriving at hospital.
A post-mortem examination carried out in New Zealand found that Mr Parker died of drowning and likely cardiac arrhythmia (heart complications).
Coroner Devonport commended Mr Rennie's and Ms Goodburn's efforts to keep Mr Parker afloat until the boat arrived.
He found there had not been sufficient staff on the boat to provide effective rescue without assistance of passengers.
"No steps appear to have been taken by the captain to ascertain if Mr Parker suffered from any medical condition, and no caution appears to have been given by the captain to Mr Parker before he commenced snorkelling.
"There is no evidence that the captain provided any medical treatment or medical equipment when Mr and Mrs Parker were assisted to the boat."
Coroner Devonport was unable to make recommendations to people outside New Zealand, but he said releasing his finding should assist in making New Zealanders aware of basic precautions while snorkelling.
"It would be of comfort to New Zealanders and others undertaking snorkelling activities in the Cook Islands if similar standards applicable in Australia and New Zealand were adopted in the Cook Islands.
