Cognitive radio sensor networks (CRSNs) is the state-of-the-art communication paradigm for power constrained short range data communication. It is one of the potential technologies adopted for Internet of Things (IoT) and other futuristic machine-to-machine-based applications. Many of these applications are power constrained and delay sensitive. Therefore, CRSN architecture must be coupled with different adaptive and robust communication schemes to take care of the delay and energy efficiency at the same time. Considering the tradeoff that exists in terms of energy efficiency and overhead delay for a given data packet length, it is proposed to transmit the physical layer payload with an optimal packet size (OPS) depending on the network condition. Furthermore, due to the cognitive feature of CRSN architecture overhead energy consumption due to channel sensing and channel handoff plays a critical role. Based on the above premises, in this paper, we propose a heuristic exhaustive search-based Algorithm-1 and a computationally efficient suboptimal low complexity Karuh-Kuhn-Tucker (KKT) condition-based Algorithm-2 to determine the OPS in CRSN architecture using variable rate m-QAM modulation. The proposed algorithms are implemented along with two main cognitive radio assisted channel access strategies based on distributed time slotted-cognitive medium access control (DTS-CMAC) and centralized common control channel-based cognitive medium access control (CC-CMAC) and their performances are compared. The simulation results reveal that proposed Algorithm-2 outperforms Algorithm-1 by a significant margin in terms of its implementation time. For the exhaustive search-based Algorithm-1 the average time consumed to determine OPS for a given number of cognitive users is 1.2 s, while for KKT-based Algorithm-2, it is of the order of 5-10 ms. CC-CMAC with OPS is most efficient in terms of overall energy consumption but incurs more delay as compared to DTS-CMAC with OPS scheme.