Yesterday we went up the 97 switchbacks. Used only hiking poles until reaching the cables (between SB #45 and 46), then got out ice axes and put on crampons. Took crampons off after about SB#48 and put the axes away shortly thereafter. The rest of the way to Trail Crest was mostly dry, although there were the usual couple of snowfields to cross higher up. We just used poles.
We contemplated putting crampons back on to cross the final snowfield below Trail Crest, but didn't. It was fine. We could have climbed up ~50' to bypass that last field completely, on rocks and dirt.
If you are a little timid/inexperienced, or if the snow is not as good as we found (we were there around 10 AM), you might use ax and crampons more than we did.
We stashed ax and crampons at Trail Crest (along with everything else except a canteen of water, a candy bar, and a parka). Did not come close to needing them from there to the summit. This is not a skills/experience issue--there is just virtually no snow past Trail Crest. There is that simple snowfield just short of the summit, but it is a piece of cake now. Or just walk around it.
My sense is that the snow level right now, from Trail Camp on up, is more like early June instead of early May. I'm planning another climb in a couple of weeks and almost certainly will not bring crampons. Undecided about the ax.
We glissaded the slope below Trail Crest. It was miserable. But we were there around 4 PM, and the cooler temperatures had created a thin crust of ice above the soft snow beneath. 3 PM and earlier would have been delightful.
This is more than you need to know, because you will undoubtedly have to go out of your way to walk on snow the end of June. But others going up soon may find the information useful.