The voyage would cover a range of activities, from learning about shark finning and other pressures on habitats, to getting up close with them in the water.
It would be based at South Africa's world-renowned "Shark Alley" - a sea channel off the Cape coast with a large fur seal colony that attracts many shark species, including huge great whites.
"I have to say that I'm not the bravest person, or someone who loves sharks, but I'm intrigued by them too, so I think going through the experience will be a great opportunity for my personal development."
Vijayakumar wanted to overcome her own fear of sharks: something that had grown with their depiction in popular culture, most recently in the hit horror film The Shallows.
"Often, they're quite misrepresented in the media, and we tend to see them as these man-eating scary creatures that are no good," she said.
"So the aim is to encounter them first-hand, appreciate the important role they play in our eco-systems, and then share our stories with the rest of the world."
She felt the messages she'd come home with would be particularly relevant to New Zealand, which is also globally renowned for its shark species diversity and cutting-edge tracking and tagging programmes.
Adventure is nothing new to Vijayakumar, who has spent weeks in the Amazon jungle with Horn on a previous trip, and once sailed a kayak built from plastic bottles down the Whanganui River to highlight New Zealand's plastic waste pollution.
"I've always had a heart for environmental issues, but still, I never thought that would mean diving with sharks."
Five reasons we need to get over our shark fear
In a world of rare but headline-grabbing shark attacks - and an endless run of shark movies - it's easy to feel scared in the water. But never mind Jaws, The Shallows or Sharknado. Shruthi Vijayakumar gives five reasons why it's sharks who are threatened.
1. Shark's don't like to eat humans. Most sharks primarily feed on smaller fish and invertebrates.
Some of the larger shark species prey on marine mammals such as seals and sea lions and studies show they respond strongly to the smell of seals and fish, but not humans.
2. You're more likely to die from heart disease, car accidents, drowning and even fireworks thank from a shark bite.
Statistically, you have about a 1 in 3,748,067 chance of dying in a shark attack, according to the International Shark Attack File of the University of Florida's Museum of Natural History.
To put that into perspective, you're at a much higher risk of dying of heart disease (a one in five chance), a car accident (a one in 84 chance), drowning at the beach (a one in 1134 chance), or even fireworks (one in 340,733) than you are of being the victim of a shark attack.
3. Humans kill A LOT more sharks than sharks kill humans
Each year sharks kill about five humans worldwide. In comparison, we're killing between 30 and 40 million sharks per year worldwide in fisheries.
In the last 20 years, sharks have been over-exploited for their fins, resulting in up to 90 per cent of the world's sharks being wiped out. One in five shark species are now threatened with extinction.
4. Sharks keep our oceans in balance
As the apex predators of the oceans, the role of sharks is to keep other marine life in healthy balance and to regulate the oceans.
Studies are already indicating that shark fishing can cause disastrous effects including the collapse of fisheries and the death of coral reefs.
5. Our economy benefits from more sharks in the ocean
The collapse of fisheries from killing sharks can have huge effects on the economy - New Zealand itself makes around $1.65 billion each year from the marine ecosystem.
In comparison, maintaining sharks in the ocean not only regulates the eco-system but also provides economic benefits through eco-tourism.
