Avi,
“the מסדר קידושיו might be מסעיה לדבר עבירה if he knows that they will do it”
This is to a degree is Am Ha’aratzes – Halachakly; unlike by Clergy and etc. by non-Jewish laws the מסדר קידושיו has no implication on the very Maaseh Kedushin. He is just performing the “how-to” directions. All a Kedushin needs are two kosher witnesses. Perhaps, you can say that about two edim, but it has nothing with Mesader Kedushin, especially if the Kedushin on its own is not the Averah.
If its like Joseph says that a non-clergy marriage is not legally married, so they should get married without any official Clergy Rabbi. They can go over all the halachas beforehand and just give a Ketubah Kedushin in the presence of two witnessed and you are married by Jewish Law. As far as the State Law goes, let them be considered as b/f g/f and file as separate.
I wonder if you all are such machmir in other Halachas as well…