There aren't many differences between Henry VII's reign and that of Edward IV in OTL. Much of his policy in administration was in effect a continuation - there were some areas where Henry went further in part because of his instability and the fact that his was a new dynasty - Henry's advantage was that many of the old families were either extinct by Edward IV's death and Richard's usurpation or were minors.
In terms of a surviving Yorkist line and a peaceful succession on Edward IV's death - then you can probably expect much the same.
Ignoring the high nobility for a moment the real power and influence at court at this period were the immediate members of the household (the gentlemen and their connections who saw the King in a very personal way every day) - it is notable that many of Edward IV's household supported rebellions against Richard III in OTL. These men were usually of means and came from the shires (they were country gentleman of some means in most cases) - they might be related to the royal family (Edward's household included his brother in law Thomas St Leger for example) or might have connections to aristocratic families etc or were long standing companions (such as Hastings brother).
These men would also serve as Justices of the Peace, would be summonsed to Parliament etc - some would rise through the ranks due to the connections they made and might indeed end up as peers or their descendants would over time due to the opportunities of being in personal attendance on the monarch.
Many of Henry's so called new men may well have come to note during Edward V's reign - Empson was a successful lawyer, knight of the Shire etc (he was in his late thirties by Henry VII's accession), Dudley was young and again a rising lawyer when he attracted Henry's attention in the 1490s but he was the son of a Knight and grandson of a baron, Brandon's family were a prominent East Anglian family and so on. John Morton (who was nearly sixty at Henry's accession) is sometime described as a new man but he became a Bishop under Edward IV.
Henry essentially continued to rely on the great families just as much as any other King and on his paternal and maternal relatives (and like the Yorkists many of those relatives were not top flight aristocrats but gentlemen or the lower nobility - the Welles, Poles etc)
The Tudor idea of new men - middle class professionals in the administration - was not a massive shift as they had always played a role - some would argue that as the role of government increased they became more necessary and therefore more visible and a lot of historians believe that to describe it as a deliberate Tudor policy is an exaggeration.
For a surviving Edward V the royal household will include the men and boys he probably grew up with members of his council in Wales and their connections along with connections of his father and mother - it becomes a personal choice of the monarch due to the close contact - these men would dress and undress him, serve him his food etc.
What he will also have is some pretty powerful and wealthy male relatives - the Duke of Gloucester and the Duke of Buckingham principally and his brother the Duke of York and Norfolk - but all will be reliant on continuing royal favour.
Edward IV was pretty conciliatory to most Lancastrians in his first reign - he was more aggressive after the brief restoration of Henry VI.
By the 1480s and Edward's death - the Courtenay's were powerless and had really vanished from the political landscape, de Vere was a wandering exile who didn't pose that much of a threat, Henry Tudor either comes home and is allowed to inherit his mother's wealth or he stays in exile along with his uncle. The Percy's had reconciled themselves to Yorkist government and the 4th Earl of Northumberland was loyal to Edward IV (though he probably resented playing second fiddle to Richard of Gloucester in the north).
You will have to decide what to do with all the dodgy legal deals Edward IV had made to enrich his wider circle - it did alienate some of the nobility who saw it as a threat to their long-term financial security.
So the Warwick estates - technically they should have gone to the male heir (son of John Neville on Warwick's death and then his heirs when he died young) with the Salisbury and Beauchamp inheritances jointly split between Warwick's daughters (and in the case of the Beauchamp inheritance it should have rested with Warwick's widow and then passed to her daughter's or their heirs)
The Holland inheritance - should have been split by very distant co-heirs but was settled on Edward's sister Anne and her daughter by her second husband - a small part was reserved for Lord Richard Grey and the rest would pass to Dorset's heir who was supposed to marry Anne St Leger.
Norfolk settled on Richard Duke of York by his father (the Howards and Berkeley co-heirs were ignored) and in the event of Anne Mowbray's death it would remain with the heirs of Edward IV.
By the 1480s many of the older generation were dying off - you will have several church appointments falling in your lap. Many of the characters that became Henry VII's court were around and served under Edward IV so don't discount people.
Edward V is also going to have surviving relatives on his maternal side which will continue to play a role in his household and government - he is also related quite closely to a number of peers through his maternal and paternal ancestry.
Edward V will also be a bit short of cash as he like his father has married a wife without any wealth - he is also stuck with providing for his mother (Elizabeth was left Sheen I think by Edward IV along with the dower settled on her which came out of crown lands), his grandmother is still living and holding her dower from the York duchy, he has numerous sisters who will need significant dowers (Edward IV intended them to have around 10,000 on their marriages but that might have to be higher if Edward V looks abroad for them) - he's might need his own Morton's fork.
