Try the ‘mercerie’ in rue de la Madeleine.  It’s alongside the rear entrance to C&A and opposite to the ‘Salle centrale’.  It’s a great favourite with dressmakers, both professional and amateur.

There’s another ‘mercerie’ off rue de la Terrassière in Eaux-Vives in (I think) rue de la Flèche, but I haven’t found their service very welocoming.

Manor and Coop-Cité also  have a smaller selection of sewing aids.  In Manor, it’s neear the net curtains and similar stuff.  There’s also a shop in Balexert  and another in Charmilles shopping centre.

If convenient, go to France, where there’s even more choice for your money..

All the best, Ritchie

Might be worth checking two places.

ONE  in Geneva >>> PB Creativity SA  at  73 rue de Lyon where they present lots of haberdashery items, not just cotton threads and buttons...;

ONE in Annemasse/France >>> LA JONQUILLE store in rue du Faucigny 12 open weekdays except Monday morning which carry a large selection

Happy sewing

I find that Manor has a decent selection of these things as well as craft items (it's in the basement level) but the store near C&A has a larger selection especially of ribbons, laces and trimmings.