lot of outsiders are prone to using that line disdainfully. .As in "eww, I don't know"

That's a freshly dumped humongous heap of bullshit. People, esp. north Indian, say it in a matter of fact way, usually with slight apologetic tone. In my entire 7 yrs here I don't think I have ever heard anyone say this with disdain and neither have I. Yes, at some points I do say this in a dismissive way but that's only with telemarketers and cross connections when the other person is shouting in Kannada and I am trying to say it's a wrong number.

Yes, they don't say it with overtly apologetic face and they shouldn't. Maybe a begging tone?

be respectful about expressing your ignorance

Right? Maybe lay on the ground straight and touch the other person's feet, start crying (maybe howling) and then somehow manage to utter the words. I guess that would serve the purpose.