Ah, but that’s the skill of “jumping octaves” for singers such as my Dad (see my previous post). You don’t have to sing the whole song an octave lower or higher: you just move between octaves when you find it either gets too high or too low for you, and keep everything within a comfortable range.
It’s also what my flute and whistle playing friends learn to do if certain notes are below their register: they just play those “lower” notes an octave above, but return to the usual tune for notes that they can play.