thanks for heads up on taking too much off.
I honestly have no idea if any of my tubes have removable presta cores, ...
I learned about removable Presta cores on a tour, I added some air with my Lezyne pump that has a chuck that threads on. The core stayed in the chuck when I moved the pump.
There are two flats on the removable cores so you can use a pliers or adjustable wrench to make them fit tighter. No flats means they are not removable. The flats are on the threaded part that your adapter would thread on to.
I know a guy that said he uses thread locker on his. Sounded like a good idea, so I now do that too but I was extremely careful to make sure that the thread locker only went on the threads, if you got any on the valve seat, that might cause a slow leak if the valve does not seat right.