Welcome to the forum.
When determining mix time, you really should know what flour you are using, and what type and length of fermentation you are doing. You noted that you will be using a cold ferment, and that probably means it will a longer fermentation period. So your mix time would be less than if you were doing a same day, room temp rise. During fermentation gluten is developed by the yeast. You also develop gluten by mixing, so over mixing before a long, cold ferment will result in an over-developed dough.
For a cold ferment in a KA mixer with C hook, I suggest mixing on the second speed for 3-5 minutes, or until the ball of dough starts to look a little smooth. If you have the larger bowl with spiral hook, then lower by one minute.
Regarding handling before bake, take it out 1-2 hours before you are ready to cook the pizza.