Im not sure if I can see Kennedy personally killing Oswald in this timeline.
Now, I could see him ordering that oswald be killed, but for him to actually pull the trigger, that would have to go down in compelete secrecy.
How many would object if he killed Oswald personally?
This is the early 1960s. People weren't as squeamish back then.
Of course, if Kennedy did it extrajudicially, THEN people would object.
On a more general note, someone used this as the POD to get First Lady Marilyn Monroe. I wonder if that would actually happen.
(Given that JFK and RFK were carrying on with Marilyn at the same time, I wonder what would happen if it were revealed the President was "sharing" the First Lady with his brother?)