The elves of Lorien certainly had military strength to fight at Mordor and also would not have been corrupted by the Ring as men would. Wouldn't the destruction of the Ring have gone more smoothly if they had carried it?
I disagree with both of your basic premises.
I don't think the Elves of Lorien had much military might at all. They had the border patrols, like the one that found the Fellowship at the borders, but hardly a sizable army. Most elves left Middle Earth by then, at the end of the First Age, and during the Second and Third Ages. In the LotR movie they show an Elven contingent coming to the aid of Helm's Deep, but this isn't based in the books, and caused quite a bit of consternation to fans when the movies came out. :)
Secondly, the Elves certainly are susceptible to the Ring's siren song. Galadriel expressly mentions her fear of being seduced by its power when Frodo and Sam talk to her in Lorien. Remember that the power of the Elves - and they still possessed much power, more than mortal Men - did not make them immune to the Ring's corruption, but quite the opposite. The more powerful they were, the more they would be tempted to use the Ring, to master it with their power, and thus fall. Tolkien specifically focused on the Hobbits' humility as the source of their resistance to the Ring's power.
'Alas, no,' said Elrond. 'We cannot use the Ruling Ring. That we now know too well. It belongs to Sauron and was made by him alone, and is altogether evil. Its strength, Boromir, is too great for anyone to wield at will, save only those who have already a great power of their own. But for them it holds an even deadlier peril. The very desire of it corrupts the heart. Consider Saruman. If any of the Wise should with this Ring overthrow the Lord of Mordor, using his own arts, he would then set himself on Sauron's throne, and yet another Dark Lord would appear...
'I pass the test,' she said. 'I will diminish, and go into the West, and remain Galadriel.'
These two quotes show that the Elves aren't immune to the powers of the Ring. If they would've been corrupted, a new powerful and potentially evil force would have risen.
Now contrast this with the hobbits who are pretty much powerless and harmless. The only one who was really corrupted by the One Ring, was Sméagol. But even he was relatively harmless as Gollum; he only became a threat after he had lost the ring.
So the Elves of Lórien or any other being with any power would have been a bad choice as a ring bearer.