[The Squatter of Amon Rûdh]

Hmm. This would be the perfect opportunity for some overly sensitive member to jump in and say that this is direct evidence that Tolkien was prejudiced against the Arabs & the Turks. I don't think this is the case, but it's still pretty interesting that he would associate the scimitar with evil goblins.

I think there's a perfect alternative to this explanation (thanks to the Silver-Shod Muse for this one):

Ooooh. Looks evil.

There you have it: a scimitar is a vicious-looking weapon, perfectly suited to the nature of goblins.
Plus it alliterates nicely with 'steel', providing a pleasingly threatening, possibly even onomatopoeic effect (the phrase 'scimitars of steel' can, with a little imagination, evoke the sound of a whetstone being drawn along a blade). I notice that even in his academic writing, Tolkien liked to use plenty of alliteration, which is one of the things that makes his essays and lectures so eminently readable.