for what its worth i would throw in my opinion hehe
I would exclude Elrond handling the ring because he himself is a ringbearer. The implications are (to me) obvious.
I could envision Gandalf handling the ring the same way as he did with Bilbo. Using an instument (like the envelope), he would be able to manipulate it out of the pocket, and replace the chain, possibly with the help of an Elrond staffer.
I love how this site makes me think about such scenarios!