Hi, there are two options for your need.
1) No Article, no record: Please set storage to none for each field and add the email field so that the form is submitted to email.
2) Articles with special permissions - you can set permission for a special group in the created article. You can manage the articles from contact form then with a search&list type in the backend.
I don´t know any possibility not to create an Article. Maybe someone else or maybe solution 1 or 2 is ok for you.
Regards
Elisa