Henry VII would have omitted the words "shedding of infants blood" from his list of accusations against Richard in 1485.
Otherwise probably not a lot. The Princes would still be dead, so that their rights would still have passed to their sister Elizabeth, who would thus still be available to marry Henry. Thus it would still be possible for Richard's Yorkist and Lancastrian opponents to unite against him.
Then the only difference would be that Richard's reputation would be less stained.
And Richard's enemies would still be able to accuse him of the deed (it's not like confessions obtained under torture haven't been faked), so Henry might not even need to omit it.
That what I thought. If there is mistrust towards Tyrell's confession, even if Buckingham had put his hand over the Bible nothing would have changed so much.
This. I mean in OTL you have Richard's defenders denigrating the confession of James Tyrell (though the existence of that is iffy).
Plus, even if you get a genuine confession out of Buckingham that is widely believed Richard is hardly in the clear. Given that Buckingham was Richard's Constable of Tower the implication is either that he was acting on Richard's orders/wishes and is now being scapegoated or that he killed two people in the king's custody (/under his protection) without permission, which doesn't say great things about Richard's authority.
And given that Richard remained almost completely silent about the deed (I've never understood that, really). Perhaps he could say that he had trusted Buckingham too much, but I don't think that would help him to avoid the criticism...
Presumably they play up the executions of Hastings, Rivers and Grey. None of them are as potent a symbol of Richard's tyranny as murdered kids but the circumstances of their deaths are still ruthless, arguably unjustified and not really judicial (especially in the case of Hastings). Richard's supposed involvement in the deaths of Edward of Westminster, Henry VI and Clarence probably get further emphasised for the same reason.
And that might be play down by stating that they were plotting to kill Richard (even if he was not the Protector yet at the time... why the heck Richard hurried Hastings death so much? Where was his common sense then?).
Well, with Clarence you have his judgment and his attainder to say "Well, you know, itwas his other brother who wanted him dead". It could be used against Elizabeth Woodville and as some kind of justification for the execution of Rivers and Grey ("they had conspired to kill my brother, they plotting to doc the same to me").
But to do all these things I've mentioned, you need something that Richard sorely missed. Either to have a good "public relations" department at hand or the will to deny it. Because he jumped at the rumours that he wanted to marry his niece.