In minimally invasive surgery, surgical instruments must enter the human body through channels with diameters of only a few millimeters to perform collaborative operations in narrow, unstructured spaces with uncertain morphologies. This presents challenges for real-time safe collaborative control due to the high risk of collisions and the high redundancy of the system. To address these challenges, a cooperative motion control method based on hybrid multi-stage optimization for ultra-minimally invasive dual-arm continuum surgical robots is proposed. First, the continuum manipulators and the environment were geometrically characterized by parametric spatial curves and voxel grid downsampling, respectively, to establish a collision detection model. Second, the Hybrid Multi-Stage Optimization with Dynamic Weight Adaptation (HMSO-DWA) algorithm was proposed. A dynamic weight objective function, based on minimum distance, was designed with a view to achieving an adaptive balance between the priorities of obstacle avoidance and task tracking. Additionally, an active safety intervention mechanism was introduced to execute strong avoidance while retaining weak target guidance under extreme risks. Simulation results showed that the collaborative task success rate reached 98.7% under dynamic obstacle interference, and the minimum inter-arm distance was maintained above 3.28 mm. Prototype experiments indicated that the tracking errors of the two arms were (0.444 ± 0.326) mm and (0.418 ± 0.273) mm, respectively. The proposed method effectively achieves safe collaborative control and trajectory tracking in constrained environments.