Sure there is. The usual map we have only shows Western Middle-Earth. Where do you think the Easterlings come from? They're way off "the map" to the east, where Asia would be in RL. Tolkien said that the Shire is roughly where England would be in RL, surprise surprise. Harad is about where one would expect North Africa to be. Hmmm. So not only do we have rough time frames (500-1040AD) for what the material culture of Middle-Earth would have looked like, but we also have rough geographical indicators too. With the exception of Avarin elves way off past the (lost?) Orocarni mountains in the distant east, it would be highly anomalous for the Eldar to be wielding swords of a scimitar-katana style. They rather epitomise the idealised, heroic "knight" (thegn, miles, whatnot) of the middle-to-late European Dark Age.
Not so incidentally, only the Orcs are mentioned carrying curved swords. Tolkien uses the word "scimitar" for it, actually. This is strongly reminiscent of the stereotypical Latin-West distinction between the cruciform sword of the Crusader, and the curved, nasty sword of the Saracen. As is much lamented elsewhere, this sort of old-school ethnic stereotyping underlies much of Tolkien's myth. So if we feel like politically correcting Middle-Earth, by all means, give the Elves (who are supposed to embody Northernness) curvy swords, just like their twisted evil imitations, the Orcs. If not, stick to the indications we get from the extensive body of texts we've got, and give'em Franconian, Carolingian, Lotharingian, Saxon swords (or thereabouts).