I think I would be inclined to save the following macro in normal.dot and
call it on entry to the first field

Sub myPrint()
Dialogs(wdDialogFilePrint).Show
End Sub

You could save it as an autoopen macro in the document, but this would
create security issues that may conspire against it being run.

A third option is to create a prominent custom toolbar in the document and
add the macro command to it.