Underwater sensor networks (UWSNs) have witnessed significant R&D attention in both academia and industry due to their growing application domains, such as border security, freight via sea or river, natural petroleum production and the fishing industry. Considering the deep underwater-oriented access constraints, energy-centric communication for the lifetime maximization of tiny sensor nodes in UWSNs is one of the key research themes in this domain. Existing literature on green UWSNs are majorly adapted from the existing techniques in traditional wireless sensor network relying on geolocation and the quality of service-centric underwater relay node selection, without paying much attention to the dynamic underwater network environments. To this end, this paper presents an adapted whale and wolf optimization-based energy and delay-centric green underwater networking framework (W-GUN). It focuses on exploiting dynamic underwater network characteristics by effectively utilizing underwater whale-centric optimization in relay node selection. Firstly, an underwater relay node optimization model is mathematically derived, focusing on underwater whale dynamics for incorporating realistic underwater characteristics in networking. Secondly, the optimization model is used to develop an adapted whale and grey wolf optimization algorithm for selecting optimal and stable relay nodes for centric underwater communication paths. Thirdly, a complete workflow of the W-GUN framework is presented with an optimization flowchart. The comparative performance evaluation attests to the benefits of the proposed framework and is compared to state-of-the-art techniques considering various metrics related to underwater network environments.