Actually, I'm not sure that Charles would have remarried at all if Diana had lived. As mentioned, he would have had to get permission from the Queen to marry again and she may have balked at the idea.
The reason? Once Diana died, Charles was effectively a widower in the eyes of the Church of England. The Queen may have seen it that Charles still had a living wife in the eyes of the Church and as Charles would one day be the head of the Church of England, she may of withheld her consent
One might say that Camilla also had a living husband when she remarried (remember they only had a blessing after the civil wedding) but a factor than might have been that Andrew Parker Bowles was a Catholic.
The Queen would not have quibbled about a royal funeral if Diana had been married to Charles at the time of her death. The Queen would not have allowed the SPencers to bury her at their estate had Charles been the widower.
Or maybe things would have gone exactly like they did. We'll never really know but I do think a remarriage for Charles would have been much more complicated had Diana lived.