Shadow Blade has a range of Self.
The PHB, pg 202, states the following under the Range entry in the Magic section:
“ Most spells have ranges expressed in feet. Some spells can target only a creature (including you) that you touch. Other spells, such as the shield spell, affect only you. These spells have a range of self.”

The literature itself, would seemingly refute your theory RSP.

The Range of “Self” also explains why the caster can reform the blade of shadow after throwing or dropping the blade.