Is he considered sinful for leaving the mosque, and is that considered a minor shirk, due to his extreme shyness of leading the prayer when the iqamah was about to be called?

It is permissible to leave a mosque to pray in another if the congregational prayer in the first mosque will not be disrupted. Reprehensible shyness is that which prevents good deeds, and one must strive against it because it is a satanic whisper. As for praiseworthy shyness, it is that which motivates one to avoid abominable acts and not fall short in acts of obedience, and it is a branch of faith. What happened is not shirk, but rather reprehensible shyness.