This was to be Parker's last fight in New Zealand before he set his sights on the UK market; indeed a victory over Fury would have heightened his profile there and made him a more lucrative prospect.
Instead, after Fury informed the WBO that he had picked up an unspecified injury and wouldn't be able to make the long-haul flight to New Zealand, Duco have been forced to search for alternatives.
If they decide to go ahead, then under the title defence rules the opponent must be ranked in the WBO's top 15, and many candidates on that list already have bouts lined up or have just fought.
The No6-ranked Dominic Breazeale is a possibility for the fact that the American, well beaten by IBF champion Anthony Joshua, doesn't have a fight lined up and should be in reasonable shape after beating Izu Ugonoh, Parker's stablemate, in an all-action scrap in Alabama in February.
Should Breazeale agree to the fight, it would be easily marketed as a "revenge match".
One boxer who has already shown an interest is Australian Lucas Browne, but the man who won the WBA "regular" title before being stripped of it due to a failed drugs test isn't an option because he isn't ranked with the WBO.
For Parker, who attended church today and spent time with his young daughter, the focus is on being prepared for any eventuality. He will continue training hard in Auckland this week in case a new opponent is found.
"These situations can be dangerous - you're bringing someone else in who you haven't prepared for physically and mentally, so we're weighing up the options," he said.
"It's an unfortunate situation. It's been hard to deal with through this whole process, but you get that in boxing. A lot of people have experienced this so it's good that we've experienced it now so if it happens again we know how to deal with it."
The Parker v Fury fight has been dogged by difficulty from the start. It went to purse bid due to the stand-off, and after that was won by Duco, the Fury camp declined to sign the contract, leading to the fight being delayed from April 1 to May 6.
Parker said: "I think they've been playing us the whole time. It's not professional, it just shows that they've got a lot to learn."
Higgins added: "That's the business we're in. You have to be philosophical. It's not for the faint-hearted."