I guess Switzerland is technically a third world country, but no-one uses the phrase to describe NATO allied status anymore. The OP means a developing country, which Switzerland isn't.
I just like to mock people who use third/first world without actually meaning it :)
But yeah my point is the same, Switzerland seems to be mostly shocked, dissapointed and loosing even more trust in the U.S. I doubt it would be much different in any case, just as it is now the U.S. is relevant enough that we _should_ care to some degree.