It may be possible that the ArcView can export its own projects (*.apr) as a shape files (*.shp). Other than that it would probably be best to contact some ESRI support or their forums and find the answer you are looking for.
Convert ArcView project to ESRI ArcView shape file.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert apr to shp on Windows
ArcGIS for Desktop Basic (formerly known as ArcView) is GIS (geographic information system) application used to visualizing, managing, creating, and analyzing geographic data.
ArcGIS for Desktop Basic is a part of the ArcGIS Desktop. ArcGIS for Desktop Basic supports creation of interactive maps, spatial analysis, GIS deployment, map viewing and navigation, map printing etc.
Convert from apr file
to shp file
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.