Shared-autonomy imitation learning lets a human correct a robot in real time, mitigating covariate-shift errors. Yet existing approaches ignore two critical factors: (i) the operator's cognitive load and (ii) the risk created by delayed or erroneous interventions. We present an uncertainty-aware shared-autonomy system in which the robot modulates its behaviour according to a learned estimate of latent-space skill uncertainty. A hierarchical policy first infers a conservative skill embedding and then decodes it into low-level actions, enabling rapid task execution while automatically slowing down when uncertainty is high. We detail a full, open-source VR-teleoperation pipeline that is compatible with multi-configuration manipulators such as UR-series arms. Experiments on pouring and pick-and-place tasks demonstrate 70-90% success in dynamic scenes with moving targets, and a qualitative study shows a marked reduction in collision events compared with a non-conservative baseline. Although a dedicated ablation that isolates uncertainty is impractical on hardware for safety and cost reasons, the reported gains in stability and operator workload already validate the design and motivate future large-scale studies.