Manual point cloud registration is often a crucial step during the mapping of 3D point clouds and usually performed on a conventional desktop setup with mouse interaction. Since 3D point clouds are inherently spatial, these 2D applications suffer from impaired depth perception and inconvenient interaction. Nonetheless, there are few efforts to improve the usability of these applications. To address this, we propose an alternative setup, consisting of a stereoscopic display and an external hand tracker, allowing for enhanced depth perception and natural interaction without the need for body-worn devices or handheld controllers. We developed interaction techniques for point cloud alignment in 3D space, including visual feedback during alignment, and implemented a proof-of-concept prototype in the context of a surgical use case. We describe the use case, design and implementation of our concepts and outline future work. Herewith we provide a user-centered alternative to desktop applications for manual point cloud registration.