Right-click on the shape, select Format Picture from the pop-up menu. select
the Web tab. You can type some text into the Alternative text box, something
like "hide me"

Then the code can be updated like this

Private Sub CommandButton1_Click()
Dim oShape as Shape

For Each oShape in ActiveDocument.Shapes
   If oShape.AlternativeText = "hide me" Then
       oShape.Visible = msoFalse
   End If
Next oShape
ActiveDocument.PrintOut Background:=False

For Each oShape in ActiveDocument.Shapes
   If oShape.AlternativeText = "hide me" Then
       oShape.Visible = msoTrue
   End If
Next oShape

End Sub