I am unaware of any other swords in Tolkien's stories that we are certain glow when enemies are near. However, there seems to be at least one other place in Tolkien's works where a sword shines blue:
Fingolfin like a shooting light/beneath a cloud, a stab of white,/sprang them aside, and Ringil drew/like ice that gleameth cold and blue,/his sword devised of elvish skill/to pierce the flesh with deadly chill.
Beren and Lúthien, "The Narrative in The Lay of Leithan to Its Termination"
"Like ice that gleameth cold and blue" seems to indicate that the sword is glowing blue, though this is solely used for a poetic description.
This is in The Lay of Leithan, which is an unfinished version of the story of Beren and Lúthien in verse. It is not generally accepted as canon since it was left unfinished and it predates the publication of the Hobbit (Tolkien abandoned it in 1931), but is has some detail that no other versions of the story have, so people can decide whether Fingolfin's sword glowing is canon.
The description of Ringil in The Silmarillion is less detailed:
[Fingolfin] drew his sword Ringil, that glittered like ice.
The Silmarillion, chapter XVIII: "Of the Ruin of Beleriand and the Fall of Fingolfin"
This doesn't suggest it glowing blue, but some sort of light is coming out from it; so The Lay of Leithan is just slightly expanding on the more-canon The Silmarillion.
If we decide to accept Ringil, Fingolfin's sword, as a fourth example of an elvish blade that glows blue when near enemies, it seems more likely that these kinds of swords were used often enough by the elves; they just were almost never mentioned.