No not a pot core, it looks just like a cotton bobbin with flanges top & bottom.
Actually when I said I've seen steel screws holding these down that might not be true, I've recently used some brass screws that are nickel plated and they look just like steel being a silver finish, thats probably what they were.
But I'll take heed and use nylon, these are fairly small choke cores.
Yes an unplanned shorted turn isnt good, unless I wanted to seriously reduce inductance.