Hi there,
It seems like you are trying to create Planet Map like Earth,
If yes then you could try it Projecting on Sphere with Cylinder UV
But as you mentioned that this method may cause some Stretching, Reason for that is it square Texture, But when when we Unwrap it, It won’t be perfect square.
So Solution will be to use Rectangular Texture (Take Example of Earth and its Texture on Atlas)
I can’t Explain all Steps here but I found this Videos that might Help you
