The sidepath on the Mendota Bridge is indeed a scenic and picturesque location. It is also, however, a section of path that is only about 8 feet wide and bordered on both sides by concrete barriers. This does not leave a lot of margin for error. So, while capturing a photo of your pal riding in front of you is a nifty souviner of your evening, taking both hands off the handlebars to take the photo might not be the most advisable course of action.
Now, assuming you choose to ignore this piece of advice, I would say that if you choose to ride no handed on the narrow, concrete lined path, you probably shouldn't do it while there is oncoming bike traffic. Just one more variable you can't control, if you catch my drift.
But, should you choose to ride with no hands on a narrow path with oncoming traffic I would advise you to make sure your skilz are such that you can actually ride your bike in a straight line. If that's beyond your capabilities, then you may want to pay extra attention to your surroundings to see whether or not you are drifting directly into the path of an oncoming cyclist (i.e. me). Any cyclist who sees another object heading straight for him or her with no apparant concerns about spatial relationships or potential for impact could find the situation somewhat alarming. And this could cause the alarmed cyclist to, once you have realized your error and corrected at the last possible moment, call you a dumbass. Loudly.