I agree with Osse.... it would be easy to change the chain without handling it directly and Elrond, who removed the tip of the Morgul blade from Frodo's shoulder would have been in very close proximity to the ring as it remained with Frodo... He probably wouldn't even have had to have had the chain specially made sinceI guess that anything manufactured by the Noldorin smiths would far out class the work of hobbits or men - only dwarves would mathc them - though of course the original chain could have been dwarvish given Bilbo's connection.
Also I think Elrond would have been the least vulnerable of the "great" to the one ring.... he would not risk "wielding" it but I think he could easily cope with such minimal contact as would be required. And it always seems to be in his nature to "do the right thing" regardless of personal feeling. Galadriel always had a desire for power and Gandalf, like Saruman, was charged specifically wih the overthrow of Sauron ... this I feel makes them more vulnerable.
Elrond did found Imladris but as a refuge not a kingdom and it was there he went rather than to Lindon after the last Alliance and though it would be a hollow title in the circumstances, he never claimed kingship, let alone High-kingship of the Noldor, which by Gil-galad's death he was surely entitled to.
Also more than anyone he knew the danger of the ring and the folly of Isildur's failure to destroy it ... had he fell victim for the lust for the ring on sight as Smeagol did - surely he would have been able to overpower Isildur at Orodruin...?
By the time of Frodo's arrival, Elrond is a healer not a warrior, a source of passive strength. My guess is that with the tweezers he used to remove the splinter of the Morgul knife he made the ring more secure.
And he had no more thought of taking it than he did at Orodruin - though what a lot of trouble that would have saved!.... but of course there would have been no book