What should someone do who remembers, while leading congregational prayers, that he is not in a state of Wudu', but is too embarrassed to appoint a successor, and this has happened to him twice?

Your continuation of prayer in congregation while in a state of ritual impurity (hadath) is a grave sin, and your prayer is invalid by the consensus of scholars. What was obligatory upon you was to immediately exit the prayer. As for the prayer of the congregants, the preponderant opinion is that it is valid, and it is more pious for them to repeat both prayers to avoid scholarly disagreement.