lesper4, I think you should stick with your current permit! Someone was up at Horseshoe Meadows last weekend, and they reported the camping area was already free of snow. You are hiking a full month from now, so you will see very little snow.
But if you do want to move the dates, you can walk in and pick up permits for Cottonwood Lakes the day before you hike. 40% of the trailhead quota is held back for walk-in people, and they become available at 11 a.m. the day before you hike.
Inyo National Forest doesn't give any preference to someone like you who has an earlier permit. And the 40% walk-in part applies to all trails except the Main Mt Whitney trail.