If you're landing at ZRH and you look like a nonthreatening (probably to be read as "white") American, the agent will quite likely not even open the cover of your passport. That's been my experience more than 50% of the time there, as recently as last August. I've taken the train across the border to Italy, and my passport was not scrutinized very carefully in that case, either. I would be most concerned about the UK, which enforces immigration rules nearly as strictly as the US.