So you want to know the order of which things happen because the word 'may' is involved with Shagrat?
If he is killed by something like
Lady of Ithilien, hence instantly going to the discard pile, then I would say his text is void and can't be used anymore.
But if he looses a skirmish by means of a strength fight, then I would say before placing the wound for loosing the skirmish, you would use shagrat's text (if you choose because it has the word 'may').