Sachartzuk (another variant transliterational spelling would be Sacharczuk) = Сахарчук in Ukrainian
Immigration records indicate that this surname was found in what was the old Vohlynskaya gubernia > Czarist Russia then Soviet Union from late 18th century to 1921. During the Interwar Period the region came under Reconstituted Poland's domain and the large gubernia was broken down into several smaller wojowodstwo/regions. Post WW2 these regions were all attached to SSR Ukraine under Soviet domain until 1991, when Ukraine became independent.
Today there are appx 1,500 people in Ukraine w/surname Сахарчук, many living in NW Ukraine, in what was once the Vohlynskaya region.
I noticed an Ivan, using your spelling of surname, heading to West Virginia. He was emigrating from a village in the Dubno district of what is today the Rivnenska oblast/region, turn of the 19th century Old Vohlynskaya gubernia
Do you have any family history that you could share? Given names, appx immigration yrs and where immigrant ancestors settled upon immigration might help pinpoint EXACT location of origin, enabling you to move your research to Ukraine.