Cojanu was also incensed by what he felt was uninformed media coverage on his fight pedigree, with Parker the red-hot favourite to win by knockout.
The 202cm fighter pointed out his sparring history with Russian ex-champion Alexander Povetkin, which he said he dominated, as evidence of his bona fides.
"You guys should go train once or twice for boxing," Cojanu told reporters. "After, throw dirt at the fighter - like with me. I never got anything for free in my life."
On the contract issue, Arthur said he'd never faced similar issues in his 47-year career in the world of boxing management.
The stress of the issue had kept him awake for more than two days, before resolving the issue with Duco on Tuesday night.
He has sought out legal advice on the matter, and alleged that both Duco and the media have already dismissed Cojanu's chances.
"We've had three different contracts in front of us, that's what really kind of irritates me - we signed the first contract before we got on the plane, we get here, (and) there's revisions made," Arthur said.
"They're looking past him. I get to the point (where) you pull a gun on me, I say pull the trigger - that's the same thing that was happening to us."
In response, Duco dead-batted the issue on Wednesday afternoon, saying only that Cojanu had signed the contract, and it was a part of boxing.
But Parker's trainer, Kevin Barry, said Cojanu's fighting words would have his WBO champion on red alert for blowback.
As possibly the largest fighter Parker has ever faced, the California-based Cojanu would offer a completely different skill-set to the ungainly Fury.
He would also be hungry for glory, knowing Saturday's fight may be his first and only opportunity to fight for a world title.
"We know what this guy's about - his experience, his capabilities," Barry said. "This is a guy who knows Joseph very well, knows me very well, knows the style of my coaching, the style of Joseph, his strengths and weaknesses.
"We know each other - that's why this fight is a very dangerous fight."
-AAP