Hand-object 3D reconstruction has become increasingly important for applications in human-robot interaction and immersive AR/VR experiences. A common approach for object-agnostic hand-object reconstruction from RGB sequences involves a two-stage pipeline: hand-object 3D tracking followed by multi-view 3D reconstruction. However, existing methods rely on keypoint detection techniques, such as Structure from Motion (SfM) and hand-keypoint optimization, which struggle with diverse object geometries, weak textures, and mutual hand-object occlusions, limiting scalability and generalization. As a key enabler to generic and seamless, non-intrusive applicability, we propose in this work a robust, keypoint detector-free approach to estimating hand-object 3D transformations from monocular motion video/images. We further integrate this with a multi-view reconstruction pipeline to accurately recover hand-object 3D shape. Our method, named HOSt3R, is unconstrained, does not rely on pre-scanned object templates or camera intrinsics, and reaches state-of-the-art performance for the tasks of object-agnostic hand-object 3D transformation and shape estimation on the SHOWMe benchmark. We also experiment on sequences from the HO3D dataset, demonstrating generalization to unseen object categories.