Uncrewed aerial vehicles (UAVs) have limited onboard computing resources and often depend heavily on external infrastructure in surveillance and search tasks. Existing studies usually rely on ground stations or fixed platforms, which restricts their applicability in infrastructure-free scenarios such as disaster response, and mainly consider local processing or binary offloading, without fully exploiting task partitionability and hybrid-mode collaboration. To address these limitations, we propose a multi-UAV collaborative hybrid-mode offloading framework, supported by lightweight route-aware communication for both single-hop and multi-hop collaboration. The framework jointly optimizes UAV trajectories, hybrid offloading decisions, and computing resource allocation to reduce search uncertainty and improve coverage. In the first stage, we develop a multi-agent deep reinforcement learning (MADRL) approach, where a graph-aware state encoder is introduced in both the actor and critic to encode inter-UAV connectivity and neighboring context under partial observability, a Dirichlet-based hybrid action space unifies discrete node selection and continuous ratio allocation, and adaptive action masking with post-normalization ensures feasible offloading decisions. In the second stage, we design an approximation-based dynamic programming (DP) task-selection algorithm for central processing unit (CPU) resource allocation to reduce decision complexity and improve optimization efficiency, and further provide theoretical support for its structured low-complexity design. Simulation results show that the proposed method significantly reduces uncertainty and improves coverage over baseline schemes in infrastructure-free environments.