We study the expansion of a cold, non-neutral ion plasma into the vacuum. The plasma is prepared by UV (355-nm) photo-ionization of Rb atoms in a magneto-optical trap. We report on the formation and persistence of shock shells in the Coulomb-exploding plasma, as well as external-field-induced plasma focusing effects. Simulated results from a trajectory model and a fluid model verify the formation of shock shells. The computational analysis allows us to calculate time- and position-dependent density, temperature, and Coulomb coupling parameter, reaffirming the presence of shock shells and strong coupling in our experiment. Among other insights, the analysis further reveals the time scale of disorder-induced heating, the build-up of pair correlations, adiabatic expansion, and ballistic cooling.