I don’t think the issue is only chilul hashem, there is certainly an inyan of keeping a low profile even if what you’re doing is perfectly ok I’m not sure what the mekor for this is [I can try to find out) but when we are in Galus we are not supposed to do anything which might anger the goyim unless of course it’s a specific mitzva. Dressing like a frum yid probably goes into the catagory of a mitzva and is a personal thing which can not be compared to lighting a public menorah, there’s no reason a goy should be angered by the way a yid dresses, however a huge menorah is inescapable and can be very annoying to a goy to see juadiasm glaring in his face like that. besides that this is something new and has never been done in history before certainly not by any gedolim whereas dressing like a yid has always been a part of yidishkeit.
(most of us even light indoors today because in Europe the goyim were hostile towards us and so it wasnt safe to light outside, Kal VaChomer a huge public Menorah.)