Nice try. Federal money was provided to dredge Charleston Harbor by the Rivers and Harbors Act.
The military had been charting and surveying the harbor even before that. The work was stopped by the outbreak of the Civil War.
The government was also building ships at Norfolk since the eighteenth century.
Pages 181-197 will inform you. A $50,000 earmark was in the act of 1852 you mentioned. The city wanted to retain control of the project, and did not begin work until the city of Charleston pledged its own $45,000 in funds in 1853.
Thus, all of the dredging equipment and later one ship were purchased or built with funds provided by the city of Charleston as well as money lent by the State of South Carolina.
On going expenses were underwritten by contracts with the city.