This study investigates the fabrication of short-wavelength infrared (SWIR) photosensitive amorphous and nanocrystalline Ge1-xSnx:H thin films by magnetron sputtering from separate Ge and Sn targets using different Ar:H mixing ratios as working gas. Amorphous Ge1-xSnx:H films have been obtained on both c-Si and fused quartz substrates at ambient temperature, while dynamic nanocrystallization occurs in-situ when the substrate temperature during deposition is raised to 200 °C. Fourier-transform infrared spectroscopy has shown the hydrogen incorporation by detecting an absorption line at 1873 cm-1, close to the value corresponding to Ge-H bonding, only in the room temperature amorphous films. Based on that, we infer that the hydrogen concentration is very low in the films deposited at high temperature. The higher concentration of hydrogen in the amorphous samples is associated with an increase of the absorption gap to 0.5eV compared to 0.3eV in the 200oC samples. In-situ (during deposition) and ex-situ (by subsequent rapid thermal annealing) nanocrystallization have been analyzed by high-resolution transmission electron microscopy, X-ray diffraction and micro-Raman spectroscopy. SWIR spectral photosensitivity up to 2.4µm was found to be more than two orders of magnitude improved in hydrogenated amorphous films with high hydrogen content, compared to the nanocrystalline ones that are weakly hydrogenated. These findings demonstrate the potential of hydrogenation to enhance the photoelectric properties of GeSn sputtering films for optoelectronic SWIR infrared applications.