That attitude has been applauded by Parker's promoter David Higgins, who told the Herald: "Every boxer is different. The fact that he wants to come four or five weeks out suggests he wants to acclimatise and avoid jetlag rather than turn up a week before and risk fatigue. It's actually quite smart.
"Peter is a very cunning trainer, as we saw when he devised Tyson's strategy against Klitschko."
Peter's nephew Tyson shocked the boxing world with his victory over Wladimir Klitschko in Germany in late 2015 - the bout which unlocked the division - and a win for Hughie over Parker would be another big surprise.
Hughie, a 22-year-old with a 20-0 professional record, looks noticeably slimmer following an intense camp that saw him training over Christmas, but Peter said he was in fact as heavy as he had ever been.
"He's actually going to weigh in about his heaviest. I think he's about 16 stone 7 pounds [106kg] at the moment, so he's going up. His weight will be over 17 stone [108kg] on fight day."
That means Parker, who weighed in at 112kg for the Ruiz fight, is likely to have a weight advantage, and Peter has no doubt about Parker's ability: "He's loose, he fires good shots from different angles. I rate the kid, he's not a world champion for nothing, and he's fought probably better opposition than any of the other young heavyweights coming up."
Higgins said demand for tickets - which went on sale on Monday - was high, particularly for corporate tables. "It's very encouraging," he said. "There is higher demand than for Joseph's last fight."