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It looks to me as though there is a part missing, with a loop at one end for the strap, a 'keyhole' shaped hole at the other, springs over the head of the fitting to allow easy removal, and is probably still on the original strap.
Something like the leather neck strap (Japan) from the store at fedka.com might work?
http://fedka.com/catalog/product_info.php?products_id=542
for what it's worth...
Colours in the butterfly picture are really nice
Does anyone know what kind of strap I need for this? or what they are called so I can search