Greencard stolen in Switzerland

I had my green card stolen this morning while traveling to Switzerland for four days! I checked online and the only way described to travel back to the US is with a "transportation letter" from the Embassy that can take up to 14 days to be issued.

A clerk at the Embassy suggested to just go back with my passport on a visa waiver program and tell the INS at immigration what happened.

That sounds a little fishy. Anybody ever done that and got away with it. I don;t mind paying all the fees etc. I just need to get back to my life and not be stuck in a foreign country for an extended period of time.