The one thing that Andrew's marrying someone else would do in this regard is to make people aware that Sarah isn't The Duchess of York and will never be again. She simply won't be able to get away with calling herself The Duchess of York when there's another woman using that title in a perfectly legal way.
Plus the coverage of the new Duchess would end up tossing Fergie out of whatever little coverage and attention she gets now. The magazines would have a new HRH to interview, cover, photograph and Fergie would end up with no more attention since she would be yesterday's news. Then of course, fi the new Duchess were beautiful, she would make Fergie even more unappealing.