Here's my guess: By July 5 almost all of the snow will be gone from the switchbacks, perhaps 95%. But that 5%--mostly just above the cables and then the final traverse to Trail Crest--will get your attention.
However, there will be nice trenches to walk in, where as many as 1000 souls will have passed through by this time. These trenches can be icy walking before the snow softens up for the day, but that shouldn't bother dayhikers. Just time it so you are on the switchbacks after 9 AM or so, and back down below them by 4 or 5. If it's a warm day, as it could very well be, this time slot could be expanded appreciably.
I sure hope I'm right, because I'm taking some flatlanders up there on an overnight climb two weeks earlier, and we won't have ice axes or crampons. I am a concerned that a couple of them may be a little timid here, but I will have a short length of rope to hopefully give them enough confidence to brave the worst parts. Still, there is a fair chance some will have to turn back.
But you don't have to depend on my guess, or anyone else's. As others have said, you should get a good idea from the reports posted a week or two earlier. In particular, look for mine on or about June 21.