Years ago I used to enjoy a service called emailias. Alas it disappeared. What emailias helped its users do was generate throwaway email addresses over which you had permanent control. The system was elaborate and nifty. You can however do something very similar with cPanel. Just set up a throwaway domain on cPanel and then go to the email forwarder setup. Should have a URL something like https://yourdomain.com:2083/frontend/x3/mail/fwds.html
Bookmark that in your browser. When you sign up for a new site, use that bookmark and create a new forwarder something like for each site for which you signup (you could use a different name but it makes it more difficult to track to whom you gave the name and we all want to KISS, don't we?).