The governor with the advice of the council is hereby authorized and empowered to undertake in cooperation with the Corps of Engineers, United States Army, a project to improve the back channels of Portsmouth Harbor for small boating. The governor, with the advice of the council is further authorized and empowered to act in behalf and for the city of Portsmouth and other public local interests as may be required in the construction of any cooperative projects thereto. Provided, however, that no action shall be taken under the authority hereof except upon a finding by the governor and council that federal funds will be made available for the projects herein described and upon a determination that the state expenditure with respect to such projects is economically justified.