I always got the sense that after Arthur's death Henry and Elizabeth worried about only having a single male heir and tried for another one. So, without Arthur's death Elizabeth might live longer (though it's worth noting none of her sisters were all that long lived- only one made it to their 40s).
A surviving Elizabeth might result in a more psychologically healthy Henry Duke of York (IOTL Henry VIII).
Without the double whammy of his wife and eldest son Henry VII could live a little longer, but not by much- he was already physically ailing.
Regarding issue for Arthur and Catherine- they obviously don't have the age differential (IOTL Catherine 'wasted' about half her potential childbearing years) but if Henry's lack of reproductive success was due to
blood group incompatibility then Arthur may suffer the same problem.
Though even if Arthur doesn't have any/many kids with Catherine he probably won't throw the whole English church into turmoil in an attempt to remarry (both because he's temperamentally different from Henry VIII and he has a male Tudor heir).
Other forms of Protestantism could filter in, but I'm not sure Arthur would be too receptive- Henry was, doctrinally, still a conservative Catholic (he just denied the Pope's authority over England), so Arthur might have a similar outlook. Though in this case 'heresy' isn't a political affront to the king (as it was for Henry as head of the English church), so maybe things would be a bit calmer (less beheadings, burnings etc.).
As for foreign affairs- the lack of a divorce regarding Catherine makes for slightly better relations with Charles V, but this won't have any huge effects- IOTL Charles was pragmatic and practised realpolitik, with the wellbeing of his aunt and cousin secondary to his own political considerations.
We can't really know what Arthur's foreign policy initiatives would be- unlike his brother, he might not be into warring with France on the pretence of England's claim there; there might be scuffling with Scotland, but in different circumstances; if Arthur and Catherine are close he might be interested in Spain, though I'm not sure he could do much there.