So two candidate towns, both in Volhynia:
Alternate names: Novi Velednyky [Ukr], Veledniki [Rus], Vlednik [Yid], Novyye Veledniki [Rus], Wieledniki [Pol], Weledniki, Vladnik
Alternate names: Volodarsk-Volynskiy [Rus], Volodarsk, Kotozovo [Rus, 1912+], Kutuzov-Volodarsk, Goroshki [Rus, before 1912], Horoshki [Yid], Horoszki [Pol]
At first Volodarsk looks best from the illegible towns on the early documents, but Louis' naturalization says he's from "Velidnik" (typed).
Looking at the Yiddish and the older pronunciations, I think Novi Velednyky is more likely.