Ah, well, I knew that long time ago, although I only checked the wiki page after I read this topic.
But I still don't think it has something to do with Serge's weapon.
Take butterfly (one of Zidane's weapon) for example, yeah, the name comes from a type of dual-wielding dagger in real world known as butterfly sword.
Maybe swallow is similar to butterfly in someway...but I still like to call it scissor blade for its shape.
the "Turning Swallow Cut" has been reconstructed as a technique involving striking downward from above and then instantly striking again in an upward motion from below.
Hmm, sounds interesting, but if I recall, both Frog and Crono have such a move, when they deal a criticla strike.
It's weird, but the swallow is even described as an oar, if you read the description. I don't know why they decided to call both Crono's sword and Serge's oar swallows, but that's the way the cookie crumbles. I'm sure tons of people think both swallows refer to the same type of weapon, but I guess it's just a word the writers happened to like. Either that or Serge's swallows refer to Zeal (as Crono's swallow came from Zeal), but it's a fairly tenuous connection...
LOL, sometimes you shouldn't take the name too serious. You know there are a lot of swords with traditional Japanese names in Castlevania series which is supposed to have a strong western background.
Warrior of Fate, an old beat'em-up arcade game with a back story of the Three Kingdoms, also has a lot of Japanese swords in it, and there's even an Excalibur...