The challenger, 41, brandished a memory stick which he said contained a video of his prediction at his press conference in London, and said the stick would be sealed in the robe he will wear into the ring at Wembley Stadium.
He bids to become a three-time world champion by claiming Joshua's IBF title and the WBA belt last held by his conqueror Tyson Fury, but despite repeatedly stating his respect for his opponent, he finally attempted to unnerve him.
At Wednesday evening's public workouts at Wembley Arena there were suggestions Klitschko deliberately finished late to ensure Joshua would be waiting to start his.
There is also a belief that he has remained so respectful towards the 27-year-old in an attempt to soften his edge before the two finally enter the ring.
Holding up a memory stick at Thursday's press conference, Klitschko said: "I recorded a video last week, and the outcome of the fight.
"My prediction, so to say. This (memory stick) is going to be in my robe, which I'm going to where this Saturday night, sealed.
"Do not ask me after the fight, 'What is on the stick?'
"The only person who's going to be able to watch it is the person who's going to buy this robe, and all the money will go to the Klitschko Foundation."
Joshua retained the same calmness he has exuded throughout the build-up to this fight - perhaps a consequence of his struggles against Dillian Whyte in 2015 when he became angry - and refused to respond to his challenger.
"I always try to strip everything back down to reality, what it really is," he said. "Just focus on it's just me and that man, coming to blows, and the best man winning.
"I take it seriously. April 29 is just another stepping stone towards greatness.
"Any fight's the right fight. I've never shied away from any fight, any opponent. There's no fear whatsoever that trembles through my body.
"(On Saturday night) I win. It's not complicated. Let's not over-think it. It's not rocket science - it's just a fight. Let's strip it right back to what it is."