Well the info on the post cards make them Straż bezpieczeństwa - That was paramilitary police formation used to disarm commoners. Each householder in Warsaw was member of this unit.
Much more probably is that they are Gwardia miejska,
Jewish unit was Gwardia miejska Starozakonna:
I cannot find much about their uniform. They were jewish people that did not want to shave their beards to the lenght to be able to serve in Gwardia narodowa.
Only unit that saw battle fought during siege of Warsaw. It did not had guns though.. at least they are not shown with any on contemporary polish illustrations.
here is another illustration that wont do you any help
It is from german source (and shows very strange uniforms and muskets)
Generally speaking - Look here
http://dziennikipowstania.pl/powstanie-listopadowe/