Shared autonomy imitation learning, in which robots share workspace with humans for learning, enables correct actions in unvisited states and the effective resolution of compounding errors through expert's corrections. However, it demands continuous human attention and supervision to lead the demonstrations, without considering the risks associated with human judgment errors and delayed interventions. This can potentially lead to high levels of fatigue for the demonstrator and the additional errors. In this work, we propose an uncertainty-aware shared autonomy system that enables the robot to infer conservative task skills considering environmental uncertainties and learning from expert demonstrations and corrections. To enhance generalization and scalability, we introduce a hierarchical structure-based skill uncertainty inference framework operating at more abstract levels. We apply this to robot motion to promote a more stable interaction. Although shared autonomy systems have demonstrated high-level results in recent research and play a critical role, specific system design details have remained elusive. This paper provides a detailed design proposal for a shared autonomy system considering various robot configurations. Furthermore, we experimentally demonstrate the system's capability to learn operational skills, even in dynamic environments with interference, through pouring and pick-and-place tasks. Our code will be released soon.