Catherine, his wife, was buried in Old Saint Marcus Cemetery per death certificate. there is no evidence of her remarrying post war so I would start there. I find nothing on line for either.

Old St. Marcus is now a city commemorative park at 6638 Gravois Rd St. Louis City.

Spelling for last name varies widely. Son George is listed as a Steck again in Old St Marcus. Stueck, Stich, Stuech, are all found as spellings in various census and other records. Son Albert was buried at Old St Marcus as well in 1890 as Steck.

As best as I can tell Charles/Karl Stick and wife Catherinna arrived from LeHarve France in 1850 via New York. Spent time in Pennsylvania where sons George and Albert were born. Subsequently moved to the Muscatine Iowa area then to St Louis by the time of 1860 census. Enrolled in Missouri 2nd Light Artillery Co D, Oct 1 1861 in St Louis. Promoted to Srgt and then was absent due to illness / consumption. Died Jan 5, 1862, presumably at home in St Louis. Smithers was the Union contract undertaker in St Louis. I am not sure he would have handled the burial as Stick was essentially excused from duty due to illness.

FWIW...
JJR