Well as I come from a family of Liverpool (Bootle) Dockers, the term "Wooly Back" goes back to the days when the Dockers used to gather in what they called the Pen. The bosses then picked who they wanted to work for them from the Pen. Now when it was especially busy the local workforce was used up so the bosses used to recruit from further afield like St Helens Haydock, Prescot and sometimes further out.
These guys where rural in those days (100 years or more ago) and need the work to supplement their farming income, thus as they where the outsiders they got the worst jobs on the docks.
This was hand-balling bales of sheeps fleeces, it was hard, oily/greasy work as the bales had to be carried on the workers backs from the quayside to the train/wagon/warehouse, hence the term woolybacks
