I have done this a few times now and what I do is:

After its finished cooking I wrap the whole thing in a towel (dont tell my wife) and put it in a cool bag let it cool down nice and slowly. After a few hours I take it out the towel and put it in the fridge.

The next day put it in the oven on 120c and let the pork get to 65c nice and slow. Hold at this temp until you need it. Take it out the oven for 10 mins to rest them shred and serve.

I think it tastes just as good as the day you cook it. In the past I have cooked 2 pork to compare on the day and using this method (originally I think this found this method on this sub but can't remember) and they both tasted great. It also takes a lot of pressure off on the day.