Simple solution fae yaz.
While the "moor" may be closed, the public footpaths and bridleways must, and will be, always open.
I've walked across moorland that's closed to public access due to grouse shooting, but stayed on the public footpath and bridleway without a problem in 40 years.
The reason that the shoots are not published in advance is so that the hunt saboteurs are denied the knowledge of where they are taking place and they can't interfere with a legitimate grouse shoot.