For Wifi I recommend ad-hoc networks, but that won't help in this case.
Your options are Line 6 MIDI Mobilizer II and a USB MIDI interface for your computer (you might not even need any cables if you buy if the right USB MIDI interface). There you could use the iRig too. For the USB MIDI interface, if you get one with the right gender MIDI cables, you don't even need cables. For example, check this one out
One option is this product
but it's pretty pricey for one iPad. On the other hand, it includes a MIDI interface and has more flexibility. Do you think you'll ever do 3 or 4 iPads? Then you need the iConnect for sure.