The Book of Navy Songs (1926) and The US Navy Song Book (1945) have got one entitled The Cruising Boys of Subdiv. Nine. (The DT didn't have subdiv according to my search and cruising got hits but not this song)

I can't sight read for voice so I will have to pick out the tune on my guitar, but the chorus seems to fit the metre of "Tramp Tramp Tramp the boys are Marching."

Frank