I’m not sure this is a halachic question, but it is a question of hanhaga.
What does our tradition say about whistling?
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.]