Hey Daniele
Maybe you can create a PDF generator on the basis of the (already ingenious) Email Designer. So that you can select the action “PDF” via the Pro Form and choose the created template with the form data as a PDF attachment or as a download.
In addition, a signature field would not be bad, the suggestion was already made. Pro Forms - Signature Field
This is just an idea because I have been confronted with this topic several times recently.
Enjoy your vacations! 
