Wish I can help you with Geneva, but I can't as I am more into the German speaking region specifically Zurich.. perhaps take up Summerrain's advice and send a PM to member Gata ?
If you didn't already know, here is a PDF
for a typical housing application ( in DE ). Notice what information they ask, with the proper answers, the chances of being selected will increase. It also shows you that one would nearly always be present here in CH with a permit in order to be first considered.
I've had refugees with a B permit paying CHF3500 for two month's of work to the agents resulting in nothing. So I am not sure how effective house hunters can be for you.
In this market esp. GVA and ZRH, it is the landlord / agency that selects the tenant, especially one that fits the bill - quiet type, learnt the local language in order to understand the house rules, debt / stain free, reliable paymaster, will blend with existing tenants in the building etc.