Best way to short these pins?
Yes, you should be able to use very fine wires, with a fine touch.

Do NOT attempt to scrape the Kapton in any way. I suggest you attempt to attach the wires on the opposite (top) side of the switch to avoid the traces. That would be the other two terminals of the switch. 

Use really fine wire (AWG30 is about right), pre-tin the wire, and use a microscope and fine clean tip unless your eyes are very good. You could ruin your camera, of course. 

The RPi should be able to do it, but how is another question. I suggest trying something like an optoisolator. An optoMOS solid-state relay would work (almost) for sure, but a cheaper optoisolator might work too (given the right polarity).