An assembly is provided for a turbine engine with an axial centerline. This assembly includes a turbine engine structure and a valve assembly. The turbine engine structure includes an outer duct wall, an inner duct wall, a first flow path and a second flow path. The inner duct wall is radially inward of the outer duct wall. The first flow path is radially inward of the inner duct wall. The second flow path is radially outward of the inner duct wall and is radially inward of the outer duct wall. The valve assembly includes a valve element and a valve actuator. The valve element is configured to regulate flow of fluid between the first flow path and the second flow path. The valve actuator is configured to move the valve element. The valve actuator is positioned entirely radially outward of the outer duct wall.