PhantomTriforce
I am a Person of Interest
To me, it's just simple math:
Zelda = Sheik;
Zelda = she;
Thus, Sheik = she.
Zelda = Sheik;
Zelda = she;
Thus, Sheik = she.
With OoT Zelda's smaller bust size, binding techniques could easily disguise them as pectoral muscles. So no, Zelda would not need magic to transform into Sheik. We can make headcanons all we like, but Occam's Razor says otherwise.
That really doesn't matter, because it's CLEARLY magic that Zelda uses. Her transformation from Sheik back into Zelda provides undeniable proof of that.