Now would a person with the “presidential class of Reagan” stopped talking, excuse himself, use a handkerchief to remove whatever and then proceed?
You're asking a really tough question. Thought the same if given the circumstances, what one would do, spit it out or swallow? (No double entendre).
I would agree with you Reagan and even GHW would have done what you described. Since Bill C took over, it's really gone down hill.
Spitting it out or doing as Cruz did would be the likely outcome and them hoping no one saw them do it.
With cameras (phones, etc) all over, it's likely someone will capture you doing something embarrassing and make it go viral which is what happened to Cruz last night.
His ego is bruised, but he will be okay.
But it's funny!