Wozniak = Возняк is a very common surname in Ukraine, especially
in Western Ukraine. It means WAGON RIDER. It is also a Polish
surname. In some cases it could even be a Jewish name.
What religion did your Grandparents practice?
Exactly where was Father born?
Why did the family emigrate in 1938?
From late 18th century to 1921 Vohlynskaya (Vohlyn) gubernia/region
belonged to the Russian Empire. From 1921-1939 it came under
the domain of Reconstituted Poland and was called Wolynskie wojowodstwo/region. Technically Poland had not existed as a geopolitical entity for the previous 125 years. After World War 2, Vohlyn became a part of SSR Ukraine, under Soviet domain, until 1991 when Ukraine became independent. During the Soviet Era, Vohlyn was redivided. Part of the northern Vohlyn (Polissia) went to Belarus. In the main it was divided into Vohlyn, Rivne, Zhytomir
and a little piece went to Khmelnytskij, all oblasts/regions in Ukraine.
You are researching a nondigitized world, where even telephones
are still a luxury in many cases.
When one has such a common surname, it is critical that
EXACT PLACE OF ORIGIN is ascertained in country of
immigration, before moving the search to a country like Ukraine.