Huluk answers Is there a mu-like term that means something like “why is this any of my business?”

[Huluk]

Are “whatever” and “I don’t care” are still too sneering for your taste? It’s intrinsically expressing a value judgment on the question if you claim it’s not relevant (for you) to know the right answer to. So I’d expect any response for it to quickly take on a sneering connotation…