A few of my friends of Hassidic background have told me that there is a minhag in the Hassidic world to not whistle with the mouth at all - weekdays, Shabbos, no difference. I am trying to find the sources and the reason for this hakpadah.
From Rav Avigdor Miller - His Life and His Revolution by Rav Yaakov Hamburger (Page 468)
He constantly warned against imitating gentile ways, even if they were not technically forbidden. He was once asked about whistling. He answered, "There is nothing wrong and there is everything wrong. There is nothing wrong because it is not ossur. There is everything wrong because it is a gentile behavior and we don't do what they do."
The poskim at http://dinonline.org/2010/04/15/whistling/ write,
"There is no source either way about whistling. It all depends on the how / why it is done, if it is done as פריקת עול it’s Assur – “Es Hashem Elokecha Tira”, but if not there is no reason to Assur. [See also Shulchan Aruch, Orach Chaim 338, where the Remo”h permits whistling on Shabbos, which implies that there is certainly no prohibition to whistle on a weekday]"
Perhaps there's a 'lo plug' across the board for certain chassidim to prevent any potential whistling issues like פריקת עול.
2) Perhaps there one must consider whether he is drawing unwanted attention to himself by making a noticeable noise. Not that it would be a lacking in modesty to whistle, but I could understand why a group would want to avoid drawing such attention themselves.