You do NOT need a minyan to get married. You need a chassan, a kallah, and 2 kosher Eidim. (It’s a good idea for at least one of those eidim to know the detailed halachos of Erusin, Kedushin etc. to be mesader)
At such a wedding, there would be no sheva berachos at bentching, since you do need 10 men for that.
That being said, this is indeed a very painful and sad situation, as historically we certainly have always celebrated chasunos with family and friends sharing, and being mesamayach chassan and kallah. May the powerful tefilos of any chassan and kallah getting married under such circumstances bring us the yeshuos we need at this time!
“מהרה ישמע בערי יהודה, ובחוצות ירושלים, קול ששון וקול שמחה, קול חתן וקול כלה”