The Swiss Embassy page says : Residents in Qatar: The applicant can send his/her documents along with his/her original passport with courier proposing a return service. The courier service will pay the application fee on his/her behalf in Kuwaiti currency and charge him/her back in Qatar. Please note that you may be requested to come to our Embassy in Kuwait or Consulate General in Manama.
http://www.eda.admin.ch/eda/en/home/reps/asia/vkwt/ref_visinf/viskwt.html

But check with the German and French missions first (Italy won't do it) - if they can do your Schengen Visa, it would always be more convenient.

Good luck.