surname: szkotek

My grandfather spelled his name :"Skotek", but it also appears as :Szkotek" on earlier records where things were recorded in polish, such as baptism records. I can not find this name anywhere on immigration search records. Even searches with sounds like, or alternate spelling come up with nothing. Can someone please help with perhaps another way to spell this?

Both spellings are extremely rare (Szkotek is used by 12 people in Poland and Skotek by 9). 7 of the Szoteks live in eastern Poland's Chelm area along today’s Ukrainian border, whilst the Skoteks are more scattered: Jelenia Góra in SW Poland (recovered territoreis) - 3, and 2 each in the Ciechanów area north of Warsaw and the central city of Łódź.
The name may have originated to mean: 1) little Scotsman, Scotsman's son or the pedlar's son (Scottish pedlars were so common in olden-day Poland that the word Szot and Szkot became synonymous for any itinerant trader regardless of nationality), 2) cowherd, from the old word for cattle skot or szkot.
The s~sz alternation is common in Polish. The tendency to pronounce sz, cz and as s, c and z is known as masurianisation (mazurzenie), although it is encountered in peasant dialects all over Poland, not only in Masuria. Such speakers would say scotka and zaba instead of szczotka (brush) and żaba (frog). And conversely, there is another linguistic phenomenon known as szadzenie (pronouncing s as sz). One example is story (drapes) pronounced as sztory).The word for lard which is now smalec in standard Polish used to be szmalec (from German/Yiddish Schmaltz), except in areas of masurianisation.
But the totally different geographic distribution of the bearers of the names Skotek and Szkotek surnames seems to indicate that these two names emerged independently.
The spelling discrepancy might have come about because your ancestor, when asked his name said either Skotek or Szkotek, and it was this written down as such by some semi-literate priest, village scribe or clerk of the Russian or German-speaking partitioning. If possible check the ancestor's Old World documents which may show the pre-arrival spelling of the name. US naturalisation papers and other US-generated documents often show what happened to the name in the post-arrival period.