Active hypothesis testing is a thoroughly studied problem that finds numerous applications in wireless communications and sensor networks. In this paper, we focus on one centralized and one decentralized problem of active hypothesis testing in the presence of an eavesdropper. For the centralized problem including a single legitimate agent, we present a new framework based on deep NeuroEvolution (NE), whereas, for the decentralized problem, we develop a novel NE-based method for solving collaborative multi-agent tasks, which, interestingly, maintains all computational benefits of our single-agent NE-based scheme. To further reduce the computational complexity of the latter scheme, a novel multi-agent joint NE and pruning framework is also designed. The superiority of the proposed NE-based evasive active hypothesis testing schemes over conventional active hypothesis testing policies, as well as learning-based methods, is validated through extensive numerical investigations in an example use case of anomaly detection over wireless sensor networks. It is demonstrated that the proposed joint optimization and pruning framework achieves nearly identical performance with its unpruned counterpart, while removing a very large percentage of redundant deep neural network weights.