I've just tested this using a point feature class in a file GDB. The point feature class contains two attributes (Name and Hyperlink). The Hyperlink field is just a Text(200) so should be compatible with shapefile limitations.
Published this up as a feature service in ArcGIS Online, open in a Map Viewer, click on the feature then click on the More info tag. The hyperlinked PDF opened in a new browser tab (Chrome) with no issues. I did not do any configuration in the Map Viewer...this appears to be default behaviour.
I did not test publishing a shapefile to ArcGIS Online...I only ever use shapefiles as a export file format and never use them for processing or data storage, the format has too many limitations. It's a simple matter to import the shapefile to a staging file gdb and publish from there.