Neilson heard surgery could be done in Auckland and, through his private health insurance with Southern Cross, had a chunk - "about half a golf ball" removed by a robot, controlled by a surgeon.
Search for "transoral robotic surgery" on YouTube and clips show a robot expertly slicing and peeling the skin from a grape, and then stitching it back on.
"Basically the surgeon sits at a console and the robot has a camera and two arms about the size of a chopstick," Neilson said.
"And at the end of those arms they've got the pinchers, the scissors ... so they can perform the surgery in a really small space."
Neilson's cancer was linked to the human papillomaviruses (HPV), as are other head and neck cancers.
HPV is extremely common and most sexually active adults are infected with HPV at some time in their lives.
In New Zealand, the Gardasil HPV vaccination is free for young people aged 9 to 26, and normally administered through school-based programmes.
It targets the types of HPV responsible for about 90 per cent of cervical and other HP-related cancers, and 90 per cent of genital warts.
Today is World Head & Neck Cancer Day.
Kiwi survivors including Neilson - who, after radiation, has been told there's a 98 per cent chance he's cured - are urging young people to get vaccinated.
Those efforts have been overseen by the Head & Neck Cancer Support Network, a patient and survivors' group that works with DHBs and health professionals to improve care.
Neilson signed the permission form for his 12-year-old son's vaccination the day before learning he had the cancer the same jab protects against. His message to other parents and young people: "just get the jab".
"It's not a pleasant cancer to go through. Post-surgery is incredibly painful. There is nothing pleasant about radiation, least of all when you're getting it on the back of the throat ... I had a very easy ride relative to a lot of people."
Dr David Grayson, clinical director of ear, nose and throat surgery at Waitemata DHB, said in the past throat cancer was normally seen in older people, including those who smoke or drank heavily.
However, in recent years there had been a huge increase in the number of young people - those in their late 30s or 40s - with throat cancer, with a good number linked to HPV.
The reasons were complex and not entirely clear, Grayson said, but it was a "no brainer" to have young people vaccinated against HPV.
"If you don't vaccinate then you are really exposing yourself to that risk of developing cancer. And the treatments for it are pretty horrific. For something that is completely preventable, it just makes such sense to have it."