This is the very first question that needs to be asked to undertake a Detranslation Project. Without an understanding of where Westron comes from, we can't possibly figure out what words it should have.
So, then: based on my reading of the source material (and of course Ardalambion), this is my chart of the principle languages of Middle-earth:
(Missing are Entish and Valarin, which are unrelated to anything, and Black Speech/Orkish, whose relations are unclear.)
Following the lines back, we see that Westron is at its heart debased Adunaic: it consists of a simplified Adunaic grammar, with a healthy helping of loan-words from the 'Dunlending' language family: the languages of southern Middle-earth during the Second Age. It also takes words from other languages (much like English), and two of its dialects have particular specialities: Gondorian Westron uses a lot of Sindarin, while Hobbitish has a big dose of Northern Mannish - the word kuduk, Hobbit, derives from that language.
Adunaic is in origin the language of the House of Hador, though it has been leavened with the Taliska of House Beor (who evacuated there after the fall of Dorthonion), and a lot of Sindarin from the Elves.
Hadorian came from the common language of the Third House, which also gave rise to Northern Mannish and its descendents; this in turn came from what I've termed Old Mannish, the original human tongue. And that? So far as we can tell, it's derived from a combination of Khuzdul - the unchanging language of the Dwarves - and one or more of the Avarin Elvish dialects (which naturally go back to the first Primitive Quendian).
Got all that? Phew - it's not easy! Luckily(?), only a few of the languages on that list are attested in any meaningful way: Sindarin, Khuzdul, Adunaic, and Primitive Quendian. By looking at the Adunaic corpus, we can hopefully trace the origins of its vocabulary back to either Primitive Quendian or Khuzdul. Words that look more 'Elvish' are probably Sindarin (or Nandorin-via-Taliska) adoptions; words that don't seem to go back to anything are unique Mannish coinings.
Once we know how the words change, we can start to translate some of our own. Will they be the actual Westron words (even assuming we can make the final leap down to Westron)? Nope! But they should be plausible alternate-universe Westron, and that's all we can really hope for.