I'm not sure what they can do with that information. Others would know better. It would depend on your nationality I suppose. The Swiss police may be able to advise you to some degree, or your embassy, as this scam is quite common.

But I guess you haven't sent any money yet? Or any bank account info? So, don't send anything and cease contact with the people. They will probably bug you for some time to come, as they got a "tug on the line" (a possible victim) and will want to follow up to get the money. Just ignore it.