I do the exact same thing as Max I use a small fine blade metal saw.. But I do use almost the same technique as Brad for filing to fit, except I place the tiny piece of tube on my 1/16 punch to hold it in a bench vice and square up or fit the ends with a small file...

And yes there are several laying in the dark corners of the shop floor I am sure...
Ever noticed that you never lose one until after, you have it about perfect for the razor????