"We don't really like that because they're not us and we're not them," insists the Wellington electrician, 30. "We're just another successful couple on TV."
But when Woman's Day mentions the big baby news Harry and Meghan recently shared, Dan swiftly backtracks. Grinning, he says, "We're happy for them, but that's not going to happen for a few years for us."
However, he and Yuki confess starting a family was something they talked about early on, during their honeymoon in Bali, with Dan admitting, "We're on the same page."
Since the Three reality series ended, he and the Japanese-born, Christchurch-based hairstylist, 32, have been getting used to a long-distance relationship.
Yuki tells, "We were so close together for four weeks, so it's really hard being apart all of a sudden – I cry all the time and he usually laughs at me – but I thought it would be harder than it is."
Nodding, Dan adds, "It does suck not being able to see Yuki every day after spending so much time together, but we're talking, calling and texting every day. The hardest thing has been keeping the relationship on the down-low until the show finishes – when you meet someone special, you want to tell the entire world."
Laughing, Yuki agrees, "We need T-shirts that say, 'We got married!'"
Yet the pair have yet to utter "the L word", with Yuki confiding, "I could say it, but he's such a Kiwi bloke and it's such a heavy word for him. I'm just going to wait. It'll come, hopefully."
In the meantime, the smitten duo have made plans to meet up over summer, with Dan confessing they're looking forward to "drinking a few too many beers or wines over fish and chips on the beach". And in November, Yuki will meet his parents.
"I'm so nervous about meeting my in-laws for the first time!" Yuki admits. "It's strange because they already know me from the show."
But Dan insists, "Mum and Dad are easy-going like me, so she's got nothing to worry about. They love how smiley and happy she is, and they're glad we get on so well together."
The couple have also talked about Dan coming face to face with his wife's family in her native Saitama, near Tokyo, possibly during next year's Rugby World Cup.
Yuki says, "My parents have met him on Skype and they're fine, but because I'm an only child, my dad wants to make sure he's OK."
Dan laughs, "Yuki's father is going to put me through a couple of hurdles, but I'll be alright. I'll try to drag my parents over to Japan too. They were already talking about going to the World Cup, so now there's a good excuse because I'm married to a Japanese girl."
Yuki says renewing their vows in a traditional Shinto wedding ceremony would be "a dream come true" and Dan is keen to don a kimono for the occasion, although he's not sure about his parents, saying, "The most Japanese my dad will get is wearing jandals. He doesn't eat sushi – just meat and two veg!"
But before they head to her homeland, Dan and Yuki will likely move in together, with one of them relocating to the other's hometown – they just don't know which way it'll go yet.
While Dan was nervous about revisiting Christchurch, where he suffered post-traumatic stress syndrome after being caught in the 2011 earthquake, he admits, "Being there with Yuki has helped a lot. It brought back memories of a rough patch of my life, but she held my hand and smiled, which was exactly what I needed. It was like that chapter of my life completely ended. I'm glad I bit the bullet and she was there with me. Now I can see it's going to be a cool city."
And Yuki is excited about exploring Wellington, a city she hasn't visited for 13 years. Dan says, "I've got to sell it to her, but at the moment, we're just going with the flow. We don't want to rush things because we haven't actually known each other long."
Yuki confesses she still has "trust issues" from a past controlling relationship, explaining, "Dan's been wonderful and I trust him, but there's still that little thing in my mind. But he talks me through them. He knows I have an issue, but he's working really hard on that."
"It's a time thing," grins Dan. "I'm just making sure I'm there for her. I know she'll get there."