I say if you're going to BBQ a shoulder, don't ruin it by making carnitas. Carnitas are good, but not as succulent and juicy as pulled pork. However what I would do is go half and half. Put half of that pulled pork aside, then, take the other half, put it on a baking sheet, spray it with apple juice, and roast it until crisp. When done mix the two together. You'll have succulent and crispy shreds all together, which will make great burritos or tacos with some dry cole slaw (just shredded cabbage and carrots, and a few dashes of red wine vinegar, salt, and pepper), hot sauce, and whatever else you add.
Make sure you let the meat plateau. While all the innards are breaking down and fat is melting the temp will not rise. It will stay like this for hours. When it begins to rise it has finished plateauing, take it out when it hits the desired final temp (195 and up a bit. Would not pass 205. 200 is good.). This is when it is pullable to make pulled pork. Take it out to early and it's slice-able and dice-able. Too late, dry.
Use a good coating of rub and keep it moist with a spritz of apple juice and you won't need any sauce. A little sugar in the rub for a good bark.
Tip: Shred half and roast while pulling the other half to keep it all warm instead of pulling it all first.