Is it permissible to say, "I am too shy to pray with shoes on," or "I am too shy to stand before Allah with shoes on," and does this statement contradict the Sunnah of the Messenger of Allah, peace and blessings be upon him?

Modesty before Allah is required, but it does not entail abandoning what Allah has legislated for a Muslim. Praying in shoes is legislated and encouraged, due to the Prophet's (peace be upon him) action and his command to differ from the Jews in their abandonment of prayer in them. It is permissible to pray in them by consensus of Muslims if their purity is known. However, if their impurity is certain, one should not pray in them until they are purified.