I can tell you that the Szikorcsin spelling is Magyar/Hungarian. The same surname is spelled Sikorc'in in Slovak.
Does the family have aconnection to Palisade Park, NY? There are Ellis Island arrival records for a couple of women going there who use the Magyar spelling of the surname. One (Aloisia) is meeting her husband Augustus. Might these be Gustav's parents?
Aloisia identifies herself as ethniclly German and gave her permanent residence as Mittweide, Germany. She said she left her mother, Anna Simek, there.
In any event, people with the different surname spellings might still be related. The spelling Sykorc'in, yielding the same pronunciation, also occurs in Slovakia today.