You're in luck. The HP ENVY 5540 All-in-One is AirPrint-enabled.
The solution to your concern is to delete that printer from Printers & Scanners, and add it again as an AirPrint printer. You must specifically indicate AirPrint. You can then delete the offending HP files as they appear. They're not necessary, and with an invalid security certificate they are not doing anything anyway.
For instructions refer to Connect an AirPrint printer to a Wi-Fi network. Sometimes it's necessary to reboot your router to recognize a newly added AirPrint device, so it couldn't hurt to do that: unplug its power cord, let it rest a moment, plug it back in.