Accurate vessel positioning is crucial for operating and maintaining wind power access systems. This study explores Lidar-Inertial Odometry (LIO) as a cost-effective alternative to traditional, expensive IMUs. In offshore wind power operations and maintenance, traditional LIO faces challenges in gravity estimation during initialization and map updating due to vessel movement and limited motion range, complicating high-dynamic scenarios. To address these issues, we propose OWP-LIO, which integrates three components: preprocessing with plane reference gravity estimation for initialization, state estimation using IEKF, and real-time map updating. Experiments in offshore environments, using traditional IMU measurements as ground truth, show that OWP-LIO, using the plane reference gravity estimation method, achieves a 24.6% reduction in RMSE in the heave direction compared to conventional methods. Additionally, land-based ablation experiments simulating highly dynamic and short-range motion demonstrate that the real-time map update reduces point cloud map size by 38.8% and processing time per frame by 8.7%, leading to decreased system resource consumption. In offshore trials, in which traditional IMU data serves as the ground truth, OWP-LIO maintains RMSE within 1 cm in heave and 0.1° in roll and pitch, while reducing costs to 9.6% of traditional IMUs.