Skullwinder's enters-the-battlefield ability targets only the card in your graveyard. If that card is an illegal target as the ability tries to resolve, the ability won't resolve and none of its effects will happen. No cards will be returned to any player's hand.

You choose the target card as you put Skullwinder's triggered ability on the stack, but you don't choose an opponent until after you have returned the card to your hand.

The chosen opponent gets to choose which card to return from their graveyard to their hand.

You may choose an opponent with no cards in their graveyard. In that case, they will not get to return anything.

Skullwinder's enters-the-battlefield ability targets only the card in your graveyard. If that card is an illegal target as the ability tries to resolve, the ability won't resolve and none of its effects will happen. No cards will be returned to any player's hand.

You choose the opponent as the ability is resolving. You may choose an opponent with no cards in their graveyard.