It depends "when" during the first skirmish
The Ruling Ring was put on.
Situation 1) If the Shadow player performed a "skirmish action" that would wound Frodo, then the Free Peoples player could respond to that by Frodo wearing the ring and taking a burden instead. At that point, skirmish actions can still take place, so
Wraith World could be played.
Situation 2) No skirmish actions take place that wound Frodo. The skirmish is then resolved and Frodo loses, he would take a wound. The Free People responds to that by Frodo wearing the ring and takes a burden instead. At this point in the skirmish, it is too late to perform any "skirmish" actions, so
Wraith World cannot be played.
I hope that clears it up for you.
