I believe cancelling a skirmish cancels all effects that happened in it... As long as the skirmish wasn't resolved, no wounds, healing, or other events that happened in the skirmish remain. The companions go back to how they were before the skirmish.
But yes, you take turns activating ablities/events, fellowship first, then shadow, then fellowship again, until you both pass. Then effects are tallied (such as wounds from damage bonuses, then deaths).