OK, how about the self timer being used? That little lever you swing round at the bottom of an old fashioned shutter, then press the shutter release and hold the stick out with the camera tied to it?
Shutter buttons on those cameras are a tiny little lever. Try aiming accurately and pushing down with a stick, it's difficult...
Also you're about 2 or 3 feet away and the walking stick has a steel tip, not recommended because of the damage you might do. Even if you could get the end of the stick there without problems due to clearance.
Of course, as I said, you could push a button back but Exaktas hadn't been invented then, nor Yashica Mats and those are all I can think of with button for the shutter like that.
Regards, David
PS On the other hand he could have been caught lashing out at the paparazzi...