Can I use the spell, Decree of Unity on Draven's signature gear, spinning axe?

Yes — Decree of Unity can kill Spinning Axe, provided the Axe is controlled by an opponent.

Spinning Axe is a Gear with the Chaos domain (Fury/Chaos), so it qualifies as an "enemy Chaos unit or gear." Attachment doesn't protect it: Gear can still be chosen or affected by spells and effects that specify Gear, and Gear can be Killed (Rules 148.1.a.3–148.1.a.4). Note the Axe's Tempory/Quick-Draw text going inactive while attached only strips the Gear of its own rules text — it doesn't change its domain or card type, which is what Decree of Unity checks.

One caveat: Decree of Unity requires an enemy target, so your own Spinning Axe can't be hit by your own Decree.