Getty of Philadelphia Window Cranks

This is an extraordinarily old handle. I doubt you'll find anything like it on the market. We may be able to find a replacement, though, since based on your description it sounds like it uses a basic spline hole design that other operator handles use to this day. Can you just tell me the diameter of the spline hole? That will help us find the best replacement, if one is even still around.

So, 1 centimeter is a little over 3/8", which is kind of a peculiar spline size. We don't have any handles with a hole in that size. 

My colleague Dave thinks that you have the old 39-045 and 39-044 Getty operators. These arms are not sold separately, I'm afraid, so the only option we may be able to provide is replacing the whole operator mechanism. Look these over and see if these match what you have now. You may also need a new 39-504 track.