He could use Lord Kilkeel instead as his courtesy title if he wanted to, but it is not terribly flattering either (think Archie Kilkeel or Archie Dumbarton).
Of course, if he became an HRH, he could be simply Archie Sussex in a British school and that would actually sound nice, I think.
Its MOST usual to use the second title.. for the heir.. but I DO think that they really didn't think it through very well, with giving Harry the Dumbarton title. I'm sure it would have provoked jokes in the press and maybe at school for his son...I cant see anything wrong with Kilkeel but if he used it, I think the press would cotton onto the fact that it was because Dumbarton sounded like Dumb or Dumbo...
However I would say he's probalby not going to be an HRH wen Charles becomes king because the Sussexes are clealry moving away from the BRF