865
But first they would need to invent some tape
(i.imgur.com)
They could have fitted the whole ring / tape / mouse assembly into a small paper bag Aragorn could have kept it in his jacket and fed it little bits of lembas on the way how lovely x
They could tie the ring to a balloon and push it along.
They could just tie it to a long string and drag it.
Tie the hands of two people together and put the ring on the rope hanging in the middle.