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
That, or Boromir would FUCK THAT MOUSE UP and take the ring for himself
The ring can obviously influence people around the ringbearer and not just the ringbearer themselves, as seen by Boromir and Faramir being tempted by it and Smeagle killing his friend for it.
Hobbits are just very good natured and resistant to the evil influence of the ring, especially Sam it seems
Now I'm picturing Boromir cornering the mouse, drawing his sword, and stating "thou hast squeaked thy last squeak" as the mouse runs back and forth in the corner, trying to escape.
It is a strange fate that we should suffer so much fear and doubt over so small a thing. Such a little thing.