Quantum resource swapping is crucial for establishing quantum networks and achieving efficient quantum communication. It allows quantum resources to be shared and allocated between nodes in a quantum network, enhancing network flexibility and quantum information processing capabilities. Quantum steering is a special type of quantum correlation that exhibits unique asymmetry compared to quantum entanglement and Bell nonlocality. This asymmetry enables quantum steering swapping to establish one-way or two-way asymmetry quantum steering between two independent optical modes, which is crucial for constructing asymmetric quantum networks. In this paper, we propose the all-optical quantum steering swapping scheme based on tripartite entangled state and bipartite entangled state. The all-optical scheme does not involve optic-electro and electro-optic conversions, but utilizes a low-noise, high bandwidth four-wave mixing process to achieve the function of Bell state measurement in traditional schemes without measurement. After the steering swapping operation, the two originally independent entangled states without direct interaction generate quantum steering. This paper specifically investigates two swapping schemes in the four-wave mixing processes, combined with linear beam splitter and nonlinear beam splitter. By analyzing the steering characteristics of the output modes, both schemes exhibited a rich variety of multipartite steering types. By adjusting the transmissivity of the linear beam splitter and the gain of the four-wave mixing process, the steering relationship can be flexibly controlled to achieve one-way and two-way asymmetry steering. This provides new possibilities for one-way quantum communication and quantum information processing, making the utilization of quantum resources more efficient and controllable. Through in-depth analysis of the steering characteristics after swapping, it was found that compared to the linear beam splitter scheme, the nonlinear beam splitter scheme not only significantly improves the ability of quantum steering, but also allows for more flexible manipulation of monogamy relations of quantum steering. By optimizing the gain parameters of the nonlinear beam splitter, precise control of the monogamy relations can be achieved over a wider range. This not only expands broader application prospects for information processing and quantum communication in quantum networks, but also establishes an important foundation for building efficient and secure quantum information processing systems.