Over the years we have been done Whitney many times in middle to late June. Often there have been medium or big snowfields left over from the winter. We never took crampons that time of year. During the day the snow is usually soft and packed down, often with huge dips called butter cups. Groups before will leave steps kicked into the snow when going up the hill above trail camp.
I haven't used Yaktrak before but they look like they would help with the traction problem you would have wearing tennis shoes on the snow. Although they don't replace crampons, they would certainly help and are very light to carry. It strikes me they are a good compromise.
