There appear to be 20 permits available for day use on May 18. These become reservable on April 1, 10 AM Eastern Time. I would get a permit, and then maybe join with others starting out that morning. Day hikers start early -- 4-5 AM.
Last year, there were about 60 unused on a similar Saturday in May (
Link to Unused Permits). If you reserve a permit, then call the Wilderness Permit number two days before, you might arrange for a night-box pickup on the 17th at the Visitor Center.