Hey, Mark!

We also coped with the same problem. The only way found:

1) Install module Document Management System (document).

2) Create directory (knowledge menu unit) or use existing one. Attach to this category required file (button "Attachments" above the form)

3) Since it was downloaded, it would generate an url. To access it: mouse right click on downloaded file - save url 

4) Add the url to the website. Pressing it will download the file (publically available).

Hey, Manuel! Regretfully, there is no enough karma to comment or answer another time. That's why this answer would be extended.

So. Programatically, it is pretty much the same. The module 'document' allows to attach files to any object, including product.product (or product.template). So you have to find it:

attachment_ids = self.env['ir.attachment'].search([('res_model','=','product.product'),('res_id','=',product.id)]). 

Where product.id - is id of needed product. E.g. you can store attachment_ids in product.product class as one2many field. After that you can get an url of any attachment. For example, for binary files:

 for attach in attachment_ids:
            url = 'https://yourcompany.com'+'/web/binary/saveas?model=ir.attachment&field=datas&filename_field=name&id='+str(attach.id)

This url may be easily added to the website product site, using foreach in product.attachment_ids