By birchas hamitzvos and birchas hanhenin we find that one should hold the item he is making a berachah on when reciting the berachah. However, we have no proof from there that a chosson should hold the ring when the mesader kiddushin recites the birchas erusin. Certainly according to the opinions that the birchas erusin is a birchas hashvach, there is no need, like the Prisha writes in regard to holding the havdolah candle, that since it is a birchas hashvach there is no need to hold it, however, even if it is a birchas hamitzvos, the ring is not the mitzvah item itself, rather, it is the item which one uses to give the women benefit of at least a perutah and through this she become mekudeshes.
There is room to argue that the chosson should hold the ring so that he has better kavonah during the birchas erusin, however, most chasanim know very well what they are standing under the chuppah for and why the birchas erusin is being recited, and it is not like a berachah on an apple which one says many times throughout his life, therefore, perhaps the extra act of holding it in his hand to help with kavonah is not needed.
Even according to the reason that we hold the mitzvah/food item to avoid unnecessary interruptions, it is clear from the Rishonim that anything that is needed for the kiddushin, such as appointing witnesses (even though it could be done before) is ok to do after the birchas erusin. Therefore, certainly taking out a ring from its case to perform kiddushin is also not considered an unnecessary interruption. I saw brought down that one time the Shevet HaLevi zt”l was mesader kiddushin and he told the chosson to hold the ring in his hand during the birchas erusin (cited in Apiryon LeShlomah, Perek 7, siman 11), however, Chazal have already told us that we can’t learn halachah from stories (Bava Basra 130b), especially when all the poskim, rishonim and achronim make no mention of such a halachah, which if it was required is something they would certainly mention, therefore, it seems that this is not the halachah and the chosson doesn’t need to hold the ring during the birchas erusin.
