I tend to remove the cores from any tubes I'm binning, so I have a small bag full of them.
( I ( well, Mrs.F ) seems to go through them at a fair rate due to cack-handed removal of the pump head after inflating, and bending the brass threaded bit to such an extent that it snaps when you straighten it. )
I've found that I have 2 slightly different sizes, the threaded bit which goes into the body is slightly longer on some than others. The wrong 'uns don't seal properly. So I'd say carefully compare the replacement with the original in terms of the thread and position of the o-ring seal.