I have never heard of the possibility of having another faction destroy the Ring, I don't think it's possible. How would they be able to get the Ring? You can't transfer it to another faction's general because he would need to be in your army/settlement. I mean, even after destroying the Ring my general still had it + Gollum as his ancillaries.
I think you only have the option of either taking or declining the quest, destroying the Ring or keeping it.
Edit: Ok, after removing the ex-ringbearer from the returning army he finally lost the Ring, Gollum and the Ring corruption trait.
And why don't you just try to get rid of it? It's a nice challenge and can make an otherwise boring game more intersting.
However, when I took the quest as Eriador I found glitch that made it a piece of cake:
The army I sent was a full stack led by Aragorn who, being a better general than the Ringbearer, led the army, which made the Ring corruption stay on level 1. Also, Mordor didn't declare war on me when I entered their territory and during the whole quest I had to fight only one battle (taking the Black Gate in order to get into Mordor). Even when I was standing near Mount Doom, Mordor didn't attack me so the quest was a big dissapointment.