You have no idea with what "everyone would have been fine with". You also don't know what it feels like to be bereaved until you are. Things you think you can cope with, eg going through with the traditional ceremonies (which is the backbone of the RF) suddenly become hard because you are tired and sad. And he got annoyed about a pen not working, he didn't punch anyone. Maybe said "underling" (your revolting word for an employee, not mine, not Charles') should have checked the thing before placing it there, which I assume was his or her job.
No, I don't think they would have cancelled any of the pomp and ceremony, because, whether you republicans like it or not, that's the stuff the public actually like. It's the stuff that makes us unique and the stuff that provides the continuity from monarch to monarch. It's the stuff that make millions flock to this country and millions watch our ceremonies. I note on Republic's website, they are quite happy to keep some of those traditions going too, so they obviously recognise the value of it. And, in any event, a "swearing in" session would have had to go ahead, just as it would in a republic if a head of state was suddenly replaces. Our "swearing in" session is set out in legal procedures that were followed after the Queen's death.