Based on the comment thread on @Knut Herrmann's answer, I believe that the solution you really want involves using "stored form". The first argument to the NotesDocument.Send() method is a boolean that specifies whether you want to store the form or not.
Normally, you would use Domino Designer to create a stored form. You would not need Designer rights to anyone's mailbox. You would just need to create an empty database of your own, and put a form into it. You woould change your code to open that database and create the document in there instead of in a mailbox database as you are doing now. (One of the other cool things about Notes is that you don't actually have to be working in a mailbox database in order to mail a document. You can mail any document from any database, as long as you put the approporiate fields into it.)
There is also a way to do this without Domino Designer, and you could even dynamically generate the form with truly custom fields that your code only discovers as it runs. You could do this with DXL, which is an XML format for describing Lotus Notes objects, including forms. You would just need some sample DXL to work from. Preferably that should be of an empty database that contains a simple form that is set up more or less in the layout that you would want, though again you would need Domino Designer for that. You could just use the same mailbox database that your code is currently using, but that will leave you with a lot of extra stuff in the DXL that doesn't need to be there; and given that you're not all that familiar with Notes, it would likely be difficult for you to navigate through it all to find what you need.
Either way, though, you could use the NotesDXLExporter class to generate the DXL file. Your code could manipulate the DXL, adding/changing elements as needed (following the pattern that you see in sample, of course), and they you could use NotesDXLImporter to create the database that your code will actually use to create the document in and mail the message with the stored form.