There are no death notices or obituaries (detailed or brief) found for this couple found in the local resource "Milwaukee's German Newspapers; an index of death notices and related items" (1844-1950).
That doesn't really infer anything since families did not regularly place notices in those years; the local German papers didn't automatically publish obituaries like many rural & small town papers; not all published editions of all papers were safely archived over the years.
However, there are Baetke Bätke and even Zanzig entries found in the index.
There's a wide variety of research strategies to follow based on local knowledge and the partially transcribed familysearch site data that will be posted here by someone else. But additional important pieces of information will be found on the civil records themselves (Johanna's last address), church records, and the Union Cemetery register which lists a Johanna for that date (dropsy; Section 1, Block 6, Lot 5), but not Joachim (inferring he died before July 1865, the earliest bur. recorded in the "B" section is July 1865). An infant grandchild named Minna Bätke was buried in that same plot: b. 13 Apr 1867-d. 13 Sep 1868, bur. Sep 5 1868.
I vote for Joachim's burial in a single grave at St. Johannes cem. or at the long-gone Gruenhagen cem. (that's bad), MAYBE Forest Home cem. That would be determined by a church burial register found at churches like St. John Luth. (8th & Vliet), Grace Luth., Trinity Luth. or other church ...? It's also worth checking for Joachim & Johanna in probate indeces, but I haven't indexed a probate notice published in the German papers.
Gary Rebholz, originator/compiler/editor, Milwaukee Wis.firstname.lastname@example.org
Indexing Milwaukee's German newspapers continuously since 2007... helping family researchers find their ancestors among Milwaukee's 99%.