Using shanties to work co-ordinate can be seen in written records,ie 1066 Norman attack on England. Duke William had a scribe make a realtime written record of his venture, The scribe noted that as the ships set sail from Normandy the sailors sang as they hoisted the sails. Then Will Shakespear The Tempest, act 1 page 1 The sailors sing Haul on the bowline. Both a little before the 1850s.
In my opinion the shanty earned its keep in the 18th 19th century when the british navy aquired sailors from many nations vessels and needed to both learn the language and co-ordinate effort. In some cases shanties were used for the crew to express their feelings to their treatment by the management. Songs like the blackball line was possibly written as early advertisment for the company.