Parker was due to defend his belt at the larger Spark Arena in downtown Auckland against Hughie Fury before the Englishman withdrew a fortnight ago with a back injury, and while Cojanu isn't the drawcard Fury is, the eyes of the boxing world will still be tuned into events in South Auckland.
It is a genuine world title fight, and Parker, who will make his walk dressed in a custom-made black robe and shorts featuring clear crystals and python skin worth nearly $10,000, is on the brink of some very big paydays as a division flourishes after being freed from the iron grip of Wladimir Klitschko.
Unification fights against Anthony Joshua and Deontay Wilder are calling, but the immediate plan is to boost Parker's profile in the UK in title defences rather than challenges.
Fury is clinging to his rights as mandatory challenger and is desperate for a piece of the action on home turf rather than in the south Pacific, but he might have to wait, and the WBO as an organisation are likely to look at a possible delay with some sympathy, should Parker's promoters ask for one.
The horse-trading will start in earnest if and when Parker gets past Cojanu, a big and powerful puncher but one who doesn't have Parker's speed of hand or foot or ability to throw the combinations the Kiwi can.
Parker and promoter Duco will likely want Liverpudlian Tony Bellew next, and perhaps as early as August. That fight is worth millions and, with heavyweight boxing on a steep upward curve in the UK following the incredible successes of Joshua and to a lesser extent the charismatic Bellew following his exploits in stopping fellow Englishman David Haye, it is one which will send Parker's profile into orbit in that part of the world.
The Furys will be aware of that, and could be persuaded to wait for their chance as a fight against Bellew or a newly boosted Parker would be far more lucrative.
Fury's trainer and father Peter appears to appreciate Parker's ability, and Hughie's heavyweight cousin Tyson has never rubbished the Kiwi like he has many of the other champions and contenders.
Parker said: "I'm glad this fight is going to be shown in the UK because not only are the doubters going to watch it but the other fighters like Bellew, Joshua and Fury so l look forward to putting on a dominant performance."
All of which means there is a great deal for Parker to lose against Cojanu, but also a great deal to win.
The Kiwi, who showed his fighting spirit and mental strength when coming from behind to beat Andy Ruiz Jr for the WBO title in Auckland late last year, is a significant part of the heavyweight equation and is nearly ready to start calling the shots abroad.
In the aftermath of Joshua's 11th-round knockout of Klitschko in their Wembley Stadium thriller, the Englishman's promoter Eddie Hearn said: "Parker is an interesting pawn in this because he's looking for that big fight. Parker might fight Wilder and he may fight Bellew. Bellew's not a future opponent for Josh."
Hearn just happens to be Bellew's promoter too.