In case it's helpful for your research, there was a German language obit. for J. L. Bednarek, but also multiple notices for a Michael Bednarik (1934) and an Anton Bednarik (1925) in the local German papers.

"Milwaukee's German Newspapers; an index of death notices and related items" (1844-1950).
Gary Rebholz, compiler/editor
Milwaukee Wis.
gary.rebholz@gmail.com
Indexing Milwaukee's German newspapers continuously since 2007 ...