I think its a neat idea. A few issues I have though are as follows:
- If it gets stuck to someone, how was it removed from Chaplin's head after he died? You would now need to explain his death as a cover up to the fact he is now a silent movie projection.
- While the projection angle is cool, I would as a reader want to understand how this works. Would the subject only exist in the presence of a movie projector? Preferably one used during that era of film?
If so how was the hat able to come into the Foundations possession? As currently it would be assumed that the last person who is wearing the hat would be Chaplin. Since he would of suffered the same fate, and became a projection. See what I mean? I don't think the hat becoming anomalous randomly and conveniently after his death will fly very well.
Personally I feel like you would be writing yourself into a corner making the hat un-removable, and the projection aspect would be a little hard as well. Another issue I have is that, how did such a famous article make its way into the possession of strangers. Let alone the Foundation.
I think something like that would of been in a museum and not really worn by anyone after the end of Chaplin's life. It kinda loops back the problem of it not being removable, and converting the subject into a 2D projection. Again, its a cool idea. But I feel like there are a lot of plot holes that make it either really hard to suspend my disbelief, or making it just a magic item.
These are not really negative aspects, so mush as obvious points of contention I see based on your description. On the positive, I like that it makes you mute. And I like that it kind of thrusts the person into a kind of "silent film world" if you will.
Maybe the hat transfers their consciousness into a silent film world, replacing their original body with some kind of comedic personality? And the original person is forever damned to live inside a silent film. This would one, incorporate Charlie Chaplin more then just name recognition (he could of been a normal person before putting on the hat). And two, would add fear factor of getting body swapped and stuck in an alternate dimension. Could get around one of the plot holes by making Chaplin the last person to wear the hat before it's contained.
Not trying to take over your idea, just bouncing idea's around to help flesh it out in my opinion.