You have presented not one word of proof that Nashville was anything other than a mainly New York owned & registered Union ship on its usual commercial business, and normally flying the Union flag.
Your claim that Nashville -- having carried US mail since at least 1855 -- no longer carried mail in 1861 is based on what evidence?
Regardless of mail, Nashville's encounter with Harriet Lane on April 11/12 was strictly a Union on Union action, having NOTHING to do with "first naval shots" of the Civil War.
Later, of course, Nashville became a highly successful Confederate blockade runner. But that was decidedly not the case during the period April 11 - 14, 1861. On those days, Nashville was simply doing what it had always done.