The question stated it was for a detail this weekend, not everyone can/will have clay to hand. I don't see the harm in using fairy as a one off, its certainly not going to ruin his paint/finish .... everyone has there own ways though
Yeah, I know what you're saying It's just that there are better ways. Granted, stock to hand is a factor (of course!), but there are shampoos that will take wax off as well intentionally. Not sure I would expect your local Halfords to stock them though.
That said, I tend to only plan a detail when I know I can do it properly and prepare with the right gear. It's almost not worth bothering with if you don't do a task properly in my own personal opinion (the threads I've seen elsewhere, involving polishing on top of un-clayed and gritty paintwork for example - pointless and a waste of time!).
Fairy/washing-up liquid can contain salts (sodium), which speed up the oxidation of paintwork, which is never good, as paintwork can become brittle and will potentially chip easier. As for surfactants, generally not good for the car at all Sure, a one-off application isn't going to accelerate this process overnight, but I wouldn't feel comfortable doing it even once.