The shocks would have nothing to do with the wandering. Shocks dampen the spring rate and that is all. Look to your tie rods, drag / center link, ball joints, control arm bushings in the front and all strut rods (4) on each side of rear and the bushings for the subframe also. Push pull and pry on everything. Watch the movement of components as someone else turns the steering wheel, look for and pauses in reaction of components. Good luck.
Chris