Any county, city, state agency or public district affected by a small flood control project referred to in Section 12750 shall give assurances satisfactory to the Secretary of the Army that the local cooperation required for such projects by Section 205 of the Flood Control Act of 1948, as amended, will be furnished by such local agency. Such agency, in conjunction with the Department of the Army, shall execute the project and may make such modifications and amendments to the plans as may be necessary to execute them for the purposes of Chapters 1 and 2 of this part.