Autonomous Underwater Vehicles (AUVs) have shown great potential for cooperative detection and reconnaissance. However, collaborative AUV communications introduce risks of exposure. In adversarial environments, achieving efficient collaboration while ensuring covert operations becomes a key challenge for underwater cooperative missions. In this paper, we propose a novel dual time-scale Hierarchical Multi-Agent Proximal Policy Optimization (H-MAPPO) framework. The high-level component determines the individuals participating in the task based on a central AUV, while the low-level component reduces exposure probabilities through power and trajectory control by the participating AUVs. Simulation results show that the proposed framework achieves rapid convergence, outperforms benchmark algorithms in terms of performance, and maximizes long-term cooperative efficiency while ensuring covert operations.