Do not address this now, but you will want to be aware of the relationship between the height of your deadwood/dead trunk and the height of your new live trunk. You do not want the two to be the same (or close to the same) because it makes your design look like a slingshot. Longer term you want one or the other to be clearly taller.
But don't shorten the deadwood now, until you decide what you want your final design to look like, and that may be determined by how your tree responds to this first initial styling. You can always remove more deadwood later on, but it is hard to put it back