A red armband? you aren't going to look like a nazi with just a red armband, maybe if you put a fucking swastika on it l, but the red arm band has also been a staple of communists militias for centuries before that. People will probably just think you're the designated driver or something and not care.
You are overestimating the historical knowledge of most societies
In Starship Troopers you have to join the military to be a citizen and vote or something like that. In AOT they have giant walls and
spoiler
The Scout Troops are the ones who go out of the walls to fight Titans. They government knows the Scouts will never succeed and it is a suicide mission so it's basically a way to get rid of the people who don't like living in the walls and don't accept the status quo
more spoilers
also the main characters overthrow the government
"Im not a Nazi, im just cosplaying a character based on the Nazis"
I feel like the wigs would tip people off they're not Nazis larping in public