In wireless security, cognitive adversaries are known to inject jamming energy on the victim's frequency band and monitor the same band for countermeasures thereby trapping the victim. Under the class of cognitive adversaries, we propose a new threat model wherein the adversary, upon executing the jamming attack, measures the long-term statistic of Kullback-Leibler Divergence (KLD) between its observations over each of the network frequencies before and after the jamming attack. To mitigate this adversary, we propose a new cooperative strategy wherein the victim takes the assistance for a helper node in the network to reliably communicate its message to the destination. The underlying idea is to appropriately split their energy and time resources such that their messages are reliably communicated without disturbing the statistical distribution of the samples in the network. We present rigorous analyses on the reliability and the covertness metrics at the destination and the adversary, respectively, and then synthesize tractable algorithms to obtain near-optimal division of resources between the victim and the helper. Finally, we show that the obtained near-optimal division of energy facilitates in deceiving the adversary with a KLD estimator.