Do you have a picture of this armband you are referring to? It might be helpful for any potential respondent.
It's a photo taken by Mendel Grossmann, titled "Two Children playing Policemen". Grossmann was a Jewish photographer who was in 1939 imprisoned in Lodz Ghetto. There he pursued his passion for photography further, creating a record of life in the Ghetto through photographing people every day and showing their situation. He was later deported and died during a death march in April 1945 after hiding thousands of his negatives.
The underlying problem in identifying what armband that is, is that Jewish Ghetoo police always wore a Star of David on their armbands and that "ẇ" is to my knowledge not a character used in Polish. The cap of his uniform resembles the so-called Blue Police, i.e. the Polish Police of the General Government under Nazi Occupation but as for what the "ẇ" stands for, I coming up blank.
