The 12-round bout at New York's Theatre at Madison Square Garden will be televised live on NBC10. The winner will meet Kubrat Pulev to become the mandatory No. 1 contender for Wladimir Klitschko's IBF title.
A former two-time world cruiserweight champion, the 36-year-old Cunningham (25-5, 12 KOs) expects to use his world-class experience to his advantage against England's 24-year-old Fury (20-0, 14 KOs).
It is just Fury's second fight outside the United Kingdom and first in the United States. Of his 20 wins, just two were against quality opponents: American Kevin Johnson and fellow Brit Dereck Chisora.
At a March news conference, Fury said Cunningham was nothing more than a light heavyweight masquerading as a heavyweight. He guaranteed to end Cunningham's career with a quick knockout.
Cunningham said it was his experience that allowed him to keep his composure.
"It's not that he got under my skin and made me say, 'Oh, I want to kill him,' " Cunningham said. "It was just, 'OK, I really want to beat this dude.' "
To beat that dude, the 6-3, 210-pound Cunningham will have to find a way to counter Fury's 6-inch height and 40-pound weight advantage.
During training, Cunningham stood on the gym floor and jabbed upward at Richardson, who stood on the ring apron. It's an old trick Richardson borrowed from another city trainer to simulate height.
"Every bit helps," Cunningham said.
Once the match starts, Cunningham said, he just has to stick to the plan.
If Fury wants to lean on him, Cunningham said, he will be ready. If he wants to box, Cunningham said, he can, too.
Richardson has a great mind, he said.
But Richardson deflected the credit. His boxer is the one who holds the keys.
"Steve Cunningham is not just an intelligent fighter. He's getting smarter," Richardson said. "He's getting smarter all the time."
Contact Matt Breen at firstname.lastname@example.org. Follow on Twitter @matt_breen.