Can I wield Spiritual Weapon in my off hand to mimic two weapon fighting?

Spiritual weapon says:

You create a floating, spectral weapon within range…

…As a bonus action on your turn, you can move the weapon up to 20 feet

This is purely for aesthetics I understand I am actually giving up some of the combat advantage of having a weapon that can move 20′ as a bonus action.
Can I instead wield the spectral weapon in my off hand and otherwise use it as intended? Is there a precedent or rule variant that says so?

The concept of wielding a Shadow Blade and spiritual weapon simultaneously is too cool for me to pass up.