As mentioned, although it's easy enough to arrange a punt via AW email, it's not an on the day type of thing, and you still need a phone to get into the venue. I've only once had a punt where it was all AW and it was a PITA, had to take my real phone in to get the door number by email.
Surely in Edinburgh the best option to punt without using a phone would be just to walk into one of the saunas?