I'm not sure if the service even exists in Switzerland, but given the cost of labor and services, it would probably be cheaper to buy new clothes and throw them away.
The better bet would be to go across the border into Saint Louis. 5-a-sec offers the service (on a pick-up/drop-off basis). You're looking for 'Linge au poids' (laundry by weight) http://www.5asec.fr/trouver-un-magas...ouis-bale.html
If you don't mind washing the clothes yourself, they also offer an 'ironing bag' service -- throw in as many pieces as fit within their bag, and they'll iron the lot for a flat fee of about EUR25. Sadly, this excludes shirts, which they can wash & iron for EUR2 each.