I agree with your interpretation. I would phrase it as:
both players pass
strength totaled
knight has higher power
minion looses/knight wins, triggering knight and mount abilities
wounds assigned one at a time*
(I think the wound from the skirmish is assigned first because it is mandatory, and then the FP player chooses the order of the two triggers, not sure about that part though)
skirmish finishes resolving (that skirmish phase ends). Characters are no longer assigned, skirmish boosts go away
*Edit to clarify: all three wounds are assigned now. First, the wound from the skirmish is put on the minion who lost, then the FP player may put 1 wound on the minion who lost and another on a minion not assigned to a skirmish in either order.