Given the high snowfall in the Sierra this year, it is unlikely that the trail will have melted out by the end of June, especially the "cables" area of the 98 Switchbacks. Look at this shot:

Now, consider that the downhill side of the trail there is a steep (45+ degree) slab of granite with 500' or more exposure. If the snowfield were still across the trail, as opposed to having melted out when Nathan and I were up there in early July, 2001, would you want to cross that stretch without ice axe, crampons
and experience???
That said, keep monitoring the list and see whether the trail has melted out or is sufficiently rutted to allow you to pass that stretch without undue risk.
My $0.02 worth says it won't be until mid-July, but that's a guess at this point in mid-May.