In WSNs, packets are delivered through mostly static shortest paths to their destination. However, static packet delivery makes WSNs highly vulnerable to traffic analysis attacks due to open area deployment. Existing defence proposals fail to achieve a balance between the protection level and the resource constraints. In this paper, we present a proactive SDN-based Route Mutation (SRRM) scheme that enables changing the routes of the multiple flows in WSNs simultaneously to defend against passive and stealthy reconnaissance and sniffer attacks while preserving reliable and energy-aware routing. Multiple routes are ranked for packet flow based on node reliability, energy consumption, link cost, and route overlapping. Our extensive simulation results show that these techniques can effectively provide route obfuscation for software-defined WSNs.