It's a bit of a nightmare finding classes for kids on Wednesdays. Fortunately, this will change in 2014 when schools will have to bring in classes for kids on Wednesdays also. During the meantime, some areas of Geneva give very reasonably priced care for kids on Wednesdays at the local centre de loisirs.
You can also try some of the private schools which might open their 'extras' classes on Wednesdays to non-attenders. One such is Decouverte, where my daughter attends on Wednesday. You can find out more here http://www.decouverte.ch/fr/extras_mercredi.html
If anybody else knows of other drop-off classes for kids on Wednesdays, particularly in the afternoon, please post a reply here.Thanks