So assuming the bullets were real and the "assassin" was a good aim:
King George VII (Prince Charles) who was still very popular at the time (think Prince William today) would benefit from a huge surge of public sympathy. The wedding would have been delayed 6 months to a year for public mourning. Charles wouldn't change his mind. Everyone around him including Prince Phillip, the Queen Mother and especially the officers of the Royal Household would be on him to give the people something to cheer for.
Now how close does Diana get to know Charles during these months (the OTL wedding was almost "shootgun" fast) is the wildcard. I think even if she finds out everything she needs to know about Camilla and all that, there'd still be tremendous pressure on her not to back out. Pretty sure this wedding still takes place but if someone were to "tap-out" it would be Diana.
The Royal Household, now focused on their young King, would put a tighter reign on both him and Diana. His ability to consort with another man's wife not in his daily circle of people would be very restricted, if by nothing else then by the schedule of daily events the Monarch has to follow. I can't see anyone in the Royal Household letting Camilla get attached to Kings' retinue. Now will he find a lady in his new circle of folks to have an affair with? Highly likely if he doesn't find love with Diana, but that would be no where near as public. No way a sitting King of the United Kingdom has a public divorce, so Diana would have to be mollified in some other, private way.
Prince Phillip stays the Duke of Edinburgh. No "need" for another title. The interesting thing with Prince Phillip is does he take a new "girlfriend"? If he does she won't be a public figure at all, but how does that go down behind the scenes? Knowing about Charles' life the way we do now, hard to see him not letting his dad get on with life.