I am glad to see we are back on topic. Let's keep it that way.
The primary purpose of the oubliette, in the game at least, is to make it highly likely that the prisoner will die in a few years without the trouble of an execution and to reduce the prisoner's stats really low while they are in prison. As far as I can tell, there is no escape difference between the oubliette and regular prison (house arrest is another matter entirely). If there is one, it's really small since I almost never lose prisoners in regular prison.
I never see your vassals being angry over an execution as squeamishness. I instead see it as worrying about your growing power. And it's only a -10 tyranny hit, so it's not that much of a problem. That's less than revoking a title.
Now, the kinslayer trait is a whole other problem. That's just your family being disgusted at your for killing a relative, and I feel that's appropriate.
"I know Uncle Edward, the Duke of Lancaster, was fond of frequenting prostitutes with webbed feet named Chloe, and he had a penchant for heresy and taking all the potato salad at family reunions, but executing him for treason is just over the top!"