If you have a base attack bonus of +1 or higher, you may draw a weapon as a free action combined with a regular move. If you have the Two-Weapon Fighting feat, you can draw two light or one-handed weapons in the time it would normally take you to draw one.
As we can see from the description, it specifies a weapon for the action you want.
If we examine wands themselves we see that all the descriptive elements fail to call it a weapon. This is further enforced by wands failing to appear on the weapon list under equipment.
Quick draw which is a continuation
Alchemical items, potions, scrolls, and wands cannot be drawn quickly using this feat.
Now, you might be able to convince your GM to treat a wand as an improvised weapon and thus can be drawn that way, but its weak reasoning because its basically a fake weapon.
Sometimes objects not crafted to be weapons nonetheless see use in combat. Because such objects are not designed for this use, any creature that uses an improvised weapon in combat is considered to be nonproficient with it and takes a –4 penalty on attack rolls made with that object. To determine the size category and appropriate damage for an improvised weapon, compare its relative size and damage potential to the weapon list to find a reasonable match. An improvised weapon scores a threat on a natural roll of 20 and deals double damage on a critical hit. An improvised thrown weapon has a range increment of 10 feet.
I have struggled with the same issue of quickly drawing a wand and not wasting so many actions, or worse switching wands and not dropping. There are no real good rules for you. Gloves of Storing would work, but its expensive for a single item.