You certainly can, but please be aware that HydroSHEDS is foremost a global product and thus its quality is designed to be appropriate for large-scale applications. When applying HydroSHEDS data locally, such as in small catchments, errors and uncertainties may be substantial and the data may not be adequate or reliable. Users are therefore advised to carefully evaluate whether a certain product is appropriate for their specific needs and purposes.
If you have additional data available for your area of interest, such as a high-resolution vectorized river network for your catchment, you can also attempt to fuse HydroSHEDS data with local information. For example, you can use the (original or conditioned) elevation data provided in HydroSHEDS and apply your own additional conditioning processes, such as stream-burning processes using the local river network, in order to produce a new hydrologically conditioned DEM. However, this requires some experience and appropriate GIS tools.