Cable-driven hyper-redundant manipulators (CDHRMs) enable unique tasks in confined spaces while presenting challenges for collision-free path planning. This article introduces a novel planning method called the stepwise follow-the-leader (SFTL) algorithm. SFTL consists of a local planner and a global planner. The local planner utilizes reinforcement learning to obtain a collision-free policy, optimizing target error, path length, angle fluctuation, and TE. The global planner incorporates an observation tree and reachability estimator to dynamically optimize extended path nodes for the local planner. The proposed sliding control points algorithm enables sequential movement along the planned path. The SFTL algorithm is applied to a coiled CDHRM and validated through simulations and practical experiments. Results show an average success rate of over 96% in various scenes, maintaining appropriate joint angles and cable tension. SFTL generates sensor-informed feasible paths, providing a robust planning framework for industrial CDHRM applications.