Q: My HP office jet 4500 wireless isn't on this list

If you're talking about the airprint list of compatible printers, then you could still make it work by having the printer attached to a computer and run software on the computer that routes transmissions to airprint through the computer to the printer.  On the mac, there's Printopia among other applications (find them at the Mac App Store).

But the bottom line is that without using some software on the computer or a special app on the device (do a search in the itunes app store for HP printing, there might be something there), you won't be able to use your printer.