printing to a non wifi printer

Hi,

Maybe.

The HP LaserJet Pro M1536dnf MFP is not mentioned in the latest About AirPrint - Apple Support article, but it was in fact listed in a very old Apple article iOS: AirPrint 101 (HT4356, February 13, 2012) as a model supporting the AirPrint technology. This may have been an old AirPrint version, and it may or may not require a printer firmware update. You may want to carry out a test with a modern iPhone or iPad.

For such a test, you would have to wire the Ethernet port of the M1536dnf printer to one of the LAN ports of your Wi-Fi router. The iPhone and the iPad would have to be wirelessly connected to the Wi-Fi network provided by that same router.

Use AirPrint to print from your iPhone or iPad - Apple Support

Generally speaking, AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections.

http://h10032.www1.hp.com/ctg/Manual/c01948866.pdf

If it's non WiFi you'll need to use a cable. If you can find a cable to do this with and an app I guess you can. But my experience is you need wireless capability.