
To avoid removing the HYPERLINK keyword, you'll have to loop through the ActiveDocument.Fields collection and test each field's Type property. If it's wdFieldHyperlink, then don't execute the Unlink for that field:
Dim fld As Field
For Each fld In ActiveDocument.Fields
If Not fld.Type = wdFieldHyperlink Then
fld.Unlink
End If
Next fld
If your documents could contain hyperlinks in storyranges other than the main one, you'll have to code for those ranges (headers, footers, footnotes, endnotes, textboxes/shapes) separately.