One doesn't need to put a huge amount of torque on the swing arm nut, but you DO want it to be well gripped by the socket so as not to round off the corners from having it slip.
As others have said, some standard, unmodified ones have thin enough sidewalls but are often 12 point sockets instead of the 6, so there is a slight possibility of less than perfect grip. The key thing is to have the end as flat as possible so that the socket slides in and grips as much of the nut surface as possible - a rounded end gives it less purchase. I sprang for one of Ed Korn's modified sockets as I don't have a lathe available to me, and my ability to do a decent job of grinding a socket uniformly is questionable.
