Checked the rules on the use of improved familiar's use of wands after a discussion earlier. Currently:
The brownie, faerie dragon, imp, lyrakien azata, mephit, quasit, sprite familiars, granted by the Improved Familiar feat, use the Biped (hands) section of the chart.
Biped (hands) familiars have all item slots which lets them use wands.
They are currently reviewing to add to this list since it hasn't been updated since 2013. So no changes so far but look forward to more options in the future!