Mr Kuik, a professional cake maker and owner of the Sweet Secret Cake House in Manurewa, had left for his hunting trip on Saturday as a treat over the Labour Weekend.
A massive search and rescue operation was carried out on Sunday when he did not return after leaving his hunting party camp site near the Waititi Stream, in the Waimana Valley, that afternoon.
Mrs Kuik admitted that after receiving a call on Monday afternoon informing her that her husband was missing, she decided not to tell Mr Kuik's elderly parents until later that day.
"They had gone out but I was home with my children. I called out to one of my boys, 'Come, we need to pray. We have to pray for daddy'.
"I didn't want his parents to worry. At that time I wasn't worried because he is very experienced. But Monday night was the hardest because the weather was bad. I kept thinking about the conditions and whether there was flooding."
Mrs Kuik thanked members of the search and rescue team, volunteers and the local community for their efforts to find and bring her husband home.
"Thank you to everyone for your prayers and support. My children are still young and I am very happy that everything is fine and he is coming home."