The undefeated Parker, who will put his WBO Oriental and PABA heavyweight titles on the line, said his shoulder was pain-free and if that continues he should be too fast and skilful for the 42-year-old Williams, who was clearly ruffled by his rival's knockout prediction.
"I'm actually happy that they've underestimated me and have put me in league with these bums," Williams, who mentioned Francois Botha and Brian Minto, said.
"I'm looking to set the record straight and leave with those championship belts.
"It gives me a bit more motivation ... We're in New Zealand, Joseph is a Kiwi, I expect this, but you need a bit of common sense and look at the background of the guys he has been fighting.
"It doesn't take a scientist to figure it out. He's never fought anyone like me."
Parker tipped the scales at 104.95, with the much shorter Williams at 120.4kg.
The South Aucklander, who has been training with Izu Ugonoh in Las Vegas, a heavyweight who will fight on tonight's undercard, looks in good shape, but Parker's tactics could be just as important.
"Out of all the fights we've had together, this would be the most detailed fight plan we've put in place, but he's implemented it very well," Barry said. "Of course the proof will be how he implements it [tonight]. He has shown me in sparring and in our skill work that he has adapted to this fight plan very smoothly.
"I'm watching him evolve and develop and improve every single camp, and I think in the next 12 to 18 months we're going to have a very special fighter."