Hmmmmm. I remember doing one show that I thought didn't have wi-fi, but now I'm not sure. I think I was able to do it through just the phone and not wi-fi. But I don't remember!! Sorry!
Then you should look at Propay, BelovedDoll. I used to use that. It's a little cardreader that you swipe the card at point of purchase and it retains the information. Then you sign in to your account on line, connect your reader and enter in all the info. There is a small fee per transaction.
Propay.com
If you look into it and like it, do NOT buy the card reader. I have one that I paid $100 for and don't use since I got my square. I would give it to you.
Let me know. I was happy with Propay. It is very very easy and straightforward.
This is the flash reader. Mine is slightly different because it's older. But still works fine.
http://www.propay.com/products-services/accept-payments/flash/