Print from iPad without AirPrint or Wi-Fi
To print to your HP printer using AirPrint you will need some kind of AirPrint server.  It is not enough to just get network connectivity to the printer, you need some software running somewhere to handle some of the communication details.  It is conceivable that someone makes a 3G WiFi router that includes AirPrint support but I think is unlikely. 

Probably your best bet is to run AirPrint software on the computer that is connected to the HP printer so that computer can act as the AirPrint server.  You can get NetGear Genie for free (though I removed it because the version I used with the OS version I was running caused my computer to crash with kernel panics, but maybe that's fixed now) or something like handyPrint (never tried it).