Hannu's suggestion is a good one for general use. ER's are cheap enough and available everywhere. The collapse allowance means you need a lot fewer of them to cover a given range.
Try to ID the collets you have to start. You can't solicit to buy if you can't identify. Then decide what you need for sizes. If you intend to use the lathe for watch/clock work, you should identify a type of collet that permits clutch/pot/step type collets.
If you only need a few, making small collets is not difficult.
If you really intend to put use the lathe routinely, perhaps re-grinding the spindle to a more common style would be an option. Or in a small lathe like that, keep the original and make a replacement.
Here is a paper on making an adaptor for common WW collets to fit in a larger spindle such as yours'
http://sherline.com/Wordpress/wp-content/uploads/2015/09/1160inst.pdf
Hardinge will make anything in work holding if you can pay the invoice.
https://www.shophardinge.com/categories.aspx?catid=126
See if anything on this list jumps out, see pages 41 - 45:
http://hardingeus.com/usr/pdf/collet/2348.pdf
For instance, 1B's have a barrel OD of 11.1mm. 2C's 11.43
If not, try using that format to describe your collet, and see if Hardinge will ID. They used to be fairly responsive. Not sure how things are these days since the auction.
smt