It can't be done this way. Wire from edge feature allows you to create wires only from edges of the solid or shell part. However you could use the point to point wire feature (Shape --> Wire --> Point to Point) to create wires between points located on the axes of these pipes. This will require some effort since you have to create the points first. In case of such complex shape of the frame I think that it would be easiest to generate wires in some CAD software and then import them to Abaqus.