Once you add an attachment to a process, it's not possible to change the database using the Designer Studio, it's no longer possible to change the attachment database.
While the Designer Studio prevents this, we are lucky that WEBCON created a transparent database and didn't artificially make it more complicated than necessary. Due to this we are able to move the attachments from one database to another and change it. Since we are modifying the database directly, you are doing this at your own risk.

You can find my approach and my test in this post. Please make sure to read also the warning section.