It wouldn't be usual for their children to be given that level of titles.
For comparison - look at the brothers of Edward VII and George V who occupied a similar level of seniority as Andrew used to.
Prince Henry Duke of Gloucester and Prince George Duke of Kent both had issue who received Prince/Princess titles in the same way as Beatrice and Eugenie did.
Prince Henry's children were Prince William of Gloucester and Prince Richard, Duke of Gloucester. Prince William died without issue. Prince Richard's children were Alexander Windsor, Earl of Ulster, Lady Davina and Lady Rose
Prince George's children were Prince Edward, Princess Alexandra and Prince Michael. Prince Edward's children are George, Earl of St Andrews, Lady Helen and Lord Nicholas Windsor. Princess Alexandra had 2 children who were given no formal titles. Prince Michael's children are Lord Frederick and Lady Gabriella.
So by comparison the maximum Beatrice and Eugenie's children might get could be getting to be Lord or Lady but they could just not be granted any title and it wouldn't be unheard of, even if Andrew had never been disgraced.