I think perhaps you are not giving colonial americans
enough credit, most of them would have been familiar with
English common law, the land owners with English land laws
and the merchants (which would include most of the land
owners shipping their produce for export) would certainly
have been conversant with the Laws of Nations to conduct
their business as maritime enterprises. They could not
afford to lose ships and crews/cargos though ignorance
of the laws.
Why? Vattel's work was philosophical and theoretical. It may be useful if one wished to argue how things ought to be, but not as a handbook of laws as they existed.