Even if we say that the birchas erusin is a birchas hashvach, and that it is clear from the Ohr Zaruah (Hilchos Krias Shema, siman 25) that by birchas hashvach there is no need for עובר לעשייתן, for the berachah to be recited close to the act of the mitzvah, who says that we shouldn’t be concerned about making unnecessary interruptions. In Hilchos Pesukei Dezimra the Mishnah Berurah (51 s.k. 4) brings from the Pri Megodim: “If one spoke idle chatter between boruch she’omer and hodu perhaps he needs to repeat boruch she’omer due to the interruption, and even one word is an interruption.” We see that even by birchas hashvach making unnecessary interruptions is a problem, therefore, perhaps this another reason to require the chosson to hold the ring.
However, we can refute the proof from pesukei dezimra, as although boruch she’omer is a birchas hashvach, it is also a berachah hasmucha lechaverta to yishtabach (see Pesochim 104b, and Tosfos d.h. chutz) therefore we don’t want any interruptions, however, birchas erusin is simply a birchas hashvach, and it is not a berachah that needs to be in close proximity to the kiddushin, it is simply a berachah that was enacted to be recited at the time of the kiddushin.