I doubt the Henry Sladek who served in 3rd MSM Calvary is one you seek:

The 1890 Special Census of Union Veterans listed his address as Paris, Monroe County, Missouri.

In 1900 he was still there, his birth listed as August 1828 Europe, immigration to USA 1853.

In the 1870-1880 censuses his birthplace is listed as Bohemia, and his sons' online death certificates also list their father as born Bohemia.

Here's his service record card:
http://www.sos.mo.gov/TIF2PDFConsumer/DispPDF.aspx?fTiff=/archives/AdjutantGeneral/Civil_War