Why do you want to cull this hen? Can't you give her away to a friend to retire and enjoy her life pottering about in their garden?. After all she has done you a great service in the past by supplying you with eggs. Sometimes the oldies just lay the odd egg a bit later in the year and that person could appreciate having the odd egg.
To tell which hen is not laying you can check the vent as those that are laying it is bigger, plus with the egg layers they tend to leave a slight slime mark on the back of the vent feathers where the egg slides down after the hen has laid it. Please reconsider dispatching this hen.
My flock is on the smaller side, so for me it's not a problem to figure that out, if I have the time to sit down and watch. Also, most of my hens have 'regular' laying times (for now), so if I'm home I can peek into the nest boxes at the times I expect a new egg, figure out who has missed based on that. If you can't do this, you could trap nest.
Here's what I've heard: If the vent is small and dry, the hen isnt laying, if on the other hand it is moist and large, the hen is probably laying. Combs can be an indication too---- pale and waxy probably not laying, red combs are a sign of laying. Hope you get the information that you need from other BYC members.
From what I understand if a hen has ever layed the pelvic bone is going to be wider if she has never layed you will only get one finger. If you are trying to find out who is spent and has layed in the past the finger test will not tell you that ( kind of like a woman who has given birth and hips widen KWIM)
So with that being said you can insert a finger into the vent and you will feel an egg forming. I would do this to all my hens for 4 days to a week so I was sure I was getting the correct hen. I did this just a few days ago because I have new hens and wanted to see which ones were laying. (in my case the finger pelvic bone test was helpful too)