The Rama y'd'303'says that should a person find someone wearing kilayim on the street unbeknownst to him he shall not tell him that on the street in order to save him from embarrassment,for he were to tell him ho would be obligated to unclothe himself of that garment.

According to the Rama it is as such even when it is kilayim min hatorah.

On this basis we may let the prayers precede as although there will be brochot le'vatalah we are saving one from embarrassment.

However the shaggas aryeh in siman 58' holds that being that we are causing one to do a maaseh avairah not in a passive state we may not allow one's embarrassment to override it. 

Still Tosafot says in Rosh Ha'Shanah 33'a' that a bracha lavatalah is a derabannan only and thus once again the embarrassment will override.

Another point to consider is that even according to those that say it is min hatorah nevertheless here it shall be de'rabanan,being that by shevuah in siman 239' there is a concept of haadom bishvuah meaning that a shvuah when sworn on the ground that it is a shevuat emet (being that he thinks the circumstances are as such) wont be considered shevuat shov or sheker.

Therefore by us being that the issur of beracah levatalah comes one and the same as by shvuat shove the same conept shall apply there.Thus,since they think they have minyan the berochot are not considered le'vatalah,and again we may let  the teffilah precede.

However i would like to conclude with a solution that should turn the entire issue derabanan and would surely won't be a problem.The one who knows the truth he shall be the sheliach tsibbur and being that he knows there is no minyan, he shall have in mind that it shall a teffilat nedavah,and then the only isssue would be the kedusha which although it is said with a minyan only is only a question of a de'rabanan.

In conclusion prayers may precede and best would be that he himself be the sheliach tsibbur.