Horseshoe Fish and Game in Merrimack (http://www.hfgclub.org/) has skeet and 5 stand. We currently have a waiting list for membership but both leagues are open to "members, perspective members and the general public". Note that Horseshoe Fish and Game in Merrimack and Horse Pond Fish and Game in Nashua are sometimes confused with each other but are different clubs.
The Lowell Sportsmen's Club in North Chelmsford has skeet, trap, and doubles trap. Open to the public Sundays at 1pm, Wednesdays at 10am, and Thursdays at 5:30pm, and no waiting list to join the club.