Is it possible for someone to reach the level of shyness (haya') of Uthman ibn Affan, may Allah be pleased with him, and can one supplicate with Zamzam water for this intention?

It is recommended for a Muslim to supplicate with comprehensive prayers for the good of this world and the hereafter, especially those authentically reported in the Qur'an and Sunnah, and to avoid contrived supplications. For asking Allah out of shyness, like the shyness of Uthman, may Allah be pleased with him, is a contrivance and an transgression in supplication.