Note: I need to apologize...I was thinking about another European nation's laws as those of Switzerland relative to filing. Switzerland has no filing requirement for Copyright. Please see below and forgive my off-hand mistake.
The first thing to understand is that there is no such thing as an "international copyright" that will protect an author's works throughout the world with a single registration (unlike the multi-jurisdictional protection provided by a patent filing under the Patent Cooperation Treaty). Copyright law is "territorial" and national in scope. Regardless of where the author lives or where the work was first published, the copyright protection afforded to a work depends on the national laws of the country in which the author seeks protection.
So, while filing for protection in Switzerland is advisable and recognized relative to the Berne Convention, it is not the equivalent per se of an US based copyright.
Every legal system is principally national; in other words, under Swiss law, works and other protected matter are only protected in Switzerland. However, international treaties have been concluded to guarantee protection at an international level. They grant Swiss authors the same level of protection as authors residing in that country as long as that country and Switzerland are signatories to the same treaty. The majority of industrialized countries have signed the most important copyright (Berne Convention ) and related rights (Rome Convention ) treaties.
There is technically no filing requirement in Switzerland for Copyright...it is copyrighted upon creation and gives 70 years after the death of the author of protection.
That said, you still need to have this work in some form of written existence and it is imperative that you have strong contractual protection around the idea (as discussed in my first response). Your idea about mailing it to yourself if another means of protection, though again, not completely fool proof.
Let me know if you have any other questions, and again, my apologies for the confusion.