Just curious, why do you say either bombs or slingshot is required for normal mode? A ranged weapon sure makes life easier but I would not call it required to complete.
You absolutely need a ranged weapon to bring down the icicles in world 2 zone 3. The only other option is the whistle’s third song, which is reached after the first point you need to do this.
This is actually false. I have completed both worlds without ranged.