I'm glad that you're so eager to purify it, but you don't need to be worried about spells backfiring from unpurified tools. Although it's highly recommended to purify tools, it isn't a requirement.
To purify it, you could wash it with moon water, or by leaving it out in the sun/moon light for a day. While doing this, visualize the wand being purified by the rays of the sun/moon.
Congrats on the new wand! :)