I wouldn't carry.
The people I have around me can't keep me 100% safe, although four deaths in a couple hundred years isn't a bad track record. By running around with a gun I'll actually make myself less safe in that situation.
There's a good chance I'll be standing there trying to shoot when the pros are trying to get me to safety. They'll put me and themselves in danger taking away the pistol and easing my ass on out the door.
Their attention will be divided because there's someone besides them waving a gun around and firing. They won't be able to do their job as well. And there's a good chance they'll plug me in the heat. They're the ones spending hours and hours every week practicing shooting and client protection. I've got more important things to do.
If someone kills all the Secret Service guards, the surrounding police officers and military types and takes out the counter snipers quickly enough that I can't get into the armored limo or head out the door and towards the horizon, well, I might as well carry a solid steel umbrella to guard against meteor strikes.
It might well cause me to stand there and get involved in a gunfight when I should be heading for safety. If I'm the President it's someone else's job to stand there and shoot and get shot while I get the hell out of there. My manly self image is one thing, but business is business.
That said, I'd use the facilities available to the Chief Executive to do whatever shooting I could squeeze into the schedule and take shameless advantage of the chance to get the very best instruction available through the top military instructors or jumping to the head of the line at Gunsite for training and photo ops.