I'd suggest approaching the judge one on one and having a friendly discussion. He may or may not want you to take a picture. It should not be about making a rule book fatter or more complicated. It is a simple matter of personal preference and communication.
Not long ago, I judged an event and later happened to be talking with an owner whose pro ran his dog in the trial. I took a picture of my score sheet and sent it from my smartphone so he could see my sheet. (sometimes a picture can tell lots of words, as the saying goes) He never posted the picture on the net anyplace and I knew he wouldn't.