There is some (very little) information out there that says the Kraftfahr (Motorized) troops of the Imperial German army wore black over black Schirmmutzen with poppy red piping. There was only one battalion in Prussia and one company sized unit in Bavaria. Some say that the Kraftfahr was not organized until 1900 while others say it came about in 1896. Either way the Schirmmutze should have a Reichs Kokarde, and, from what I gather, a Kraftfahr Mutze should have either a Prussian or Bavarian Kokarde. I can find nothing on a red and silver Kokarde for these.
It seems that the more common Schirmmutze worn by motorized troops is made of oil cloth, not wool.
If I had to guess I would think that your Schirmmutze was used by a police or fire department. My second guess would be that it was used by a veteran's organization.
John
