I believe the Empire Sniper uses the larger 11/16 valve. The WGP guns that used 11/16 valves were the Trillys, the 2k5 Black Magic midblock and the JOLEs. All other WGP cockers used a 9/16 valve. The 9/16 valve used a jam nut, the 11/16 valve did not.
I'm not absolutely sure on this, but I believe the CCM S5 and SS-25 (just a mini'd S5) used the 11/16 valve and didn't need a jam nut. That would be why the kit didn't come with one.
The Sniper does not even have a jam nut to steal.