Most likely not*
The rules for special materials state the following:
Most materials are metals; they can be used to make metal weapons and armor. The GM is the final arbiter of what items can be made using a material
While "Most materials are metals" is not a useful statement, because obviously some are not, this strongly implies that special materials substitute similar normal materials. Special woods substitute normal wood, and special metals substitute normal metals. As Handwraps are "embroidered strips of cloth", metal can't be used to replace the cloth.
*Now, your GM might disagree and might allow it (The rules for special materials state that a GM is the final arbiter), but they should probably adhere to the pretty obvious intention behind the special materials. as laid out with the example of the special metals.