Peter Seeger sang The Golden Vanity on The Almanac Singers' 1941 album Deep Sea Chanteys and Whaling Ballads with the first verse including the phrase 'put (out) to sea':

There was a lofty ship, and she put out to sea
And the name of the ship was the Golden Vanity
And she sailed upon the low and lonesome low
As she sailed upon the lonesome sea

Anyway, the first verse of Wellerman is cobbled together from borrowed phrases, two lines from The Golden Vanity, one line from Outward Bound, and one line from Blow Boys Blow. Very lazy songwriter.