The first-ever Broadway production of Dames at Sea will drop anchor at the Helen Hayes Theatre this season. Directed and choreographed by three-time Tony nominee Randy Skinner, the tap-happy tuner will begin performances on September 24 and officially open on October 22. No word yet on casting for the show, which features a book and lyrics by George Haimsohn and Robin Miller, along with music by Jim Wise. Skinner&rs…