What do the paparazzi hate more than anything?

Someone with a better shot than theirs.  They want to have an "exclusive" shot.  Something new.  Something controversial.  Something nobody else has.  More than anything they want to capture intense emotion.  A moment of truth.  Don't give it to them.  Don't talk to them.  Don't let them provoke you.  Being enraged only gives them something of value.  Instead, render their photos common, meaningless, and useless by taking the high road and immediately publishing something better yourself.  The more generous you are, the more control you gain.

By working together we can make it better.  Your fans will be educated about appropriate behavior and the paparazzi will eventually learn that there is no longer money in it.