I would plan the route using the komoot app (setting the travel mode to walking is important) and not rely on a map from 2017.

I would probably end in Sachsenhausen near Schweizer Platz and eat something at either one of the simple pizza places or at one of the local cider taverns like the Gemalte Haus. Back to the airport from Südbahnhof station.

I don't have much experience with showering in the Sen lounges in FRA (as I am based in FRA). But it is my understanding there can sometimes be long-ish wait lists for the showers. Thus, I'd say be back at the airport no later than 7:30 PM.

Oh, and check the S-Bahn connection on the day of travel--currently there is construction affecting the airport lines which sometimes get re-routed through Südbahnhof. (There is also an express bus X61 available from Südbahnhof.)