Q: A printer that works exclusively with iPad Air 2 without a computer

AirPrint capable printers should be able to do that.

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

and AirPrint supporting printers will require not presence of a computer so you're in the clear..

When setting up your Airprint printer one of the requirements is that they are in the same wifi network.  On a cheap printer like mine that means you need to run a start up disc in a laptop connected to the printer to enter the wifi information. On a more expensive printer you can enter the info right on the printer, no start up disc required. In the instructions it will say something like "Make sure they're both on the same wifi network." and is often misunderstood.

The Airprint printer is a printer. Airprint just means you can print from a iPad. Once set up it doesn't need a computer. Unfortunately the lower end models need a computer to input the wifi address and passcode.