Hi Kidneys59 and welcome to the forum,
It will be a couple of weeks more until I have access to my reference books but I do have a pdf file on my laptop which I’ve just uploaded to my site that may help. I’m posting the link to it below. The LC and SC should be for large collet and small collet. If you scroll down to where it says Hamilton 18s and look at the factory number column you will find 126. You will see under the column labeled HS (hairspring) the dimensions of .97 for LC and .77 for SC..you should be able to determine which staff you’ll need by checking for those collet dimensions on your old staff. I know the pivot sizes are a little different than what it shows in the chart but the collet dimensions should still apply.
Here’s the link:
I hope this helps Kidneys59,