Is the GSI Hydrographic chart using WGS84 for the geographic coordinate reference system (datum)? Or some other GeoCRS that isn't the same as the input raster?
If so, you'll either need to identify the actual geographic CRS of the raster, and use the Define Projection Tool or the raster's property page to update the coordinate reference system information OR define a custom geographic transformation using that tool and then project the raster including the geographic transformation.
Melita