How to install dryer ducting inside existing wall?
If the wall is non-load bearing, you may not need to do anything. If
the wall is loadbearing, you should probably not do this at all, or you should exit the cavity space through a side, not through the top.
It would be a heck of a lot easier to do with the wall open.
I would in general prefer a vent that only goes directly through the wall (shortest-way) rather than one enclosed in it for a significant distance. Dryer ducts need maintenance, and a duct buried in the wall is hard to check, and harder to maintain/repair/replace/inspect than one that is exposed. If enclosing it for a significant distance, I'd want 2x6 or double 2x3 or 2x4 (separate studs for each side with space in the middle) wall so as not to have the duct not quite fit. And I would make certain that I had adequate access points to get a cleaning rod through the entire duct without a great deal of fuss and bother.


Best dryer vent I ever had was not quite the best possible, but it was close - one elbow and 2 feet of rigid duct right out the wall. If you can back right up to the outside wall and have 6" of duct, you'e about as good as it gets. If you need a long  tortuous duct path to get the dryer vented outside, you may want to rethink where the laundry is located - there is probably a better location for it (and perhaps one closer to where dirty clothes, sheets and towels are generated, and clean ones stored, than many houses have due to people following old habits of laundry placement that make no sense without servants, laundry chutes, and dumbwaiters...)