I agree with John to wait until you are to serve the pork to then pull it, but you have to factor in the time it takes to do that. Pulling the pork takes a lot of hand work and it is intensive, probably 20 to 30 minutes of labor on a big shoulder, just as much on a few small butts.
Be sure to factor in the pulling time, for me, 30 minutes on a big joint. I also like to let the joint rest for at least an hour because it is so damn hot, after 20 something hours, it will be at the cooker temperature inside, but still, this makes the best pulled pork.
Myself, I use to regular table forks to tear away at it and shred it up. Works good for me.