I don't think a skirmish would miraculously be canceled once a minion is already assigned.
Think of it this way, I suppose - making a minion lose fierce with
Eowyn, Northwoman during the fierce assignment phase by assigning it to the Ring-bearer wouldn't cancel that skirmish, would it? That just seems silly. Making a minion lose fierce with
Phial of Galadriel, Star-Glass doesn't cancel skirmishes, either, right?
Though I don't think there's a definitive ruling on this it's probably safe to assume the skirmish still happens.