No you dont have to send the documents to Kuwait. Now that the Schengen Visa holders can enter Switzerland, you can very well use some of the other EU embassies here.

I just came from switzerland, my first touch point was Austria (their emabassy too is in Kuwait), so I used the German Embassy to get the schengen visa, after a week in Austria we used the schengen visa to fly from austria to switzerland.

Rgds,

J.J