The U S Census records contain many references to Henry Rademacher; there are 16 in the year 1900 alone, none of which appeared to be your person. However, I did locate Henry J. Rademacher in the 1920 Census in Milwaukee - T-625, Roll 2003, Page 3 & E D 211, Sheet 3B. Ward 18.
The condition of the record via the Internet is very poor. However, Henry J.(63), Ottilie (57) and son, Romuald (27) reside at 695, the street name is illegible. All were born in Wisconsin, the H & W's parents were born in Germany.

Additionally, I found the death notice of Henry S. Rademacher in the March 15, 1964 Chicago Tribune in which it's stated that he died the previous day. He was age 74 years and lived at 1700 Manchester Rd. in Wheaton, IL. He was a retired attorney and left a widow, Laura, sons Perrin G. and Richard C. and a daughter, Mrs. Joan Klem. Services were held in the chapel of the Trinity Episcopal Church, Wheaton. He was the grandfather of nine.

Can I be of additional help? Robert J. Niersbach