Is there a history of big ships on the high seas in Manchester?
No high seas but plenty of history of big ocean going ships due to the Manchester Ship Canal linking the city to the Irish Sea via Liverpool.
And from memory the first ship to sail along it was a three masted sailing ship in 1894, the year City was founded and noted on the badge along with a sailing ship and steering wheel, so I am willing to wager that is the story behind that badge.
Tenuous enough link though as not many people outside the city would readily associate Manchester with a maritime connection.