Despite their potential, markerless hand tracking technologies are not yet applied in practice to the diagnosis or monitoring of the activity in inflammatory musculoskeletal diseases. One reason is that the focus of most methods lies in the reconstruction of coarse, plausible poses for gesture recognition or AR/VR applications, whereas in the clinical context, accurate, interpretable, and reliable results are required. Therefore, we propose ShaRPy, the first RGB-D Shape Reconstruction and hand Pose tracking system, which provides uncertainty estimates of the computed pose to guide clinical decision-making. Our method requires only a light-weight setup with a single consumer-level RGB-D camera yet it is able to distinguish similar poses with only small joint angle deviations. This is achieved by combining a data-driven dense correspondence predictor with traditional energy minimization, optimizing for both, pose and hand shape parameters. We evaluate ShaRPy on a keypoint detection benchmark and show qualitative results on recordings of a patient.