Sorry if I'm being too irksome, but some words seem to have a faint/weak h sound [Hmm... I can - it is a final voiceless sigh. I was going to say that the "h" in Bah! is slightly less than the one in Ah!... ] and others, like ooh, don't. So what I'm understanding is that they have (naturally) the weak sound because the puff of air produces it, for they are interjections/onomatopoeics, right? adding an h was just a convention?
By the way I tried listening to them, some voices produce a subtle puff at the end, others don't.