Iki wo tsuku is what I wrote initially wheere its more like taking a breather rather than focusing physically on taking a breath. I don’t think it’s ambiguous really and when it’s people letting out a breath/exhaling I would say to read it as haku.
EDIT: oh wow I just realized I completely deleted what I said earlier. I think you have it backwards and when they want you to read it as tsuku there will be furigana or just no kanji more likely tbh rather than the other way around. Although I’ll tell you, the only time I have ever seen it as tsuku it never had kanji to begin with and it’s always like 息をつく暇がない. Googling it seems to be in agreement that tsuku is mental nuance and haku is physical lung nuance


