avhaben:- The Minjan is only required for the Nissuin.
The Kiddushin only requires 2 Kosher Eidim. The Messader Kiddushin could also double function as 1 of the 2 Eidim, and failing that, the Chosson can recite the Birkas Kiddushin, since it really is the Chosson’s Berocho, but not to embarrass a Chosson who cannot read Ivrit, this Berocho is nowadays always recited by a Messader Kiddushin.