I am a Cudek. I live in Ottawa, Canada. I doubt the information I have is related to your query but I thought I would respond. Here is what little I know:
In Canada our spelling is Cudeck. My grandfather Joseph Cudeck was born April 30, 1909 in Czestochowa, Poland. He arrived in Toronto, Canada just before WWII.
I remember stories that the original last name was indeed Tzudik but that the name was anglicized for immigration purposes. I also know that there were/are
Cudeks living in Paris and they had/have a fur factory.
Joseph Cudeck (d.June 4, 1985) married Eva Rose (Jan 20, 1909-Nov 11, 1989). They had 2 children: Sydney (Nov 28/36-Oct 31/76) and Jerry (May 2/47-Nov 24/97). Sydney married Anne Gliklich (Apr 5/38-Dec 20/20). They had 2 children. Denise (b.July 11/64) and Ken (b.Nov 9/66). As far as I know, we (Denise and Ken) are the last surviving Cudeck's in Canada. We have no children. Jerry Cudeck embraced the Chasidic culture late in his life and married twice. The second marriage produced a daughter who I believe lives in New York. She is probably in her 20's or 30's by now and is married.
Feel free to contact me again if you need more information. I hope this information was helpful for you. Shabbat Shalom.
Denise Lascelle (nee Cudeck)