Given the choice, she would ask for more than a marriage behind closed doors. In another world, where secrets were unnecessary, she would have the world follow her to the altar, for what has she to be ashamed of in Antonio? It is fear, not shame, that drives them to this, for they contain each their own honour, he as much as she.
Still: she is a prince, here as everywhere. Even were she not, her word as a woman were sufficient for this, and they are ministers of their own marriage. This is enough, so she will take it.