Print from iPad without AirPrint or Wi-Fi Consider the following configuration


I have a Wi-Fi iPad without 3G support. 
I also have an HP printer that doesn't not have Wi-Fi capabilities.
My printer supports USB.
I am planning to buy a 3G Wi-Fi Router.


I understand, in order to print from my iPad to a printer I need an AirPrint-compatible printer. I am also aware that for certain selected printers (let say mine is one of those privilege) you can use iOS Apps from OEM such that you can print from your iPad. But even to use it, I need a Wi-Fi enabled printer.

I am planning to purchase a 3G Wi-Fi router so that I can connect my iPad outside a Wi-Fi network. 

Now from here I was wondering, if I can use such a 3G Wi-Fi router which suppose has a USB Port to connect my printer and provide me the option to print from my iPad?

Note
I am not sure if this question fits in Ask Different as my target device is an Apple Device but even then there is more than that this question would cover. So in case if you feel this question fits there, feel free to migrate.
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).