Well....Hamilton for all his faults was not interested in spereading democracy (a concept that he despised) througho force of arms. That idea began under Wilson.
There is a difference between spreading "democracy" and spreading representaive government.
And Hamilton, as commander of the US Armed Forces during the Quasi-War, did suggest seizing both the Louisiana Territory and Mexico by force - implying that he saw Mexico as potentially being absorbed into the US or being organized as an ally along the lines of the USA.