It is possible that WA will extradite. It typically depends on their funds. My suggestion is to contact your attorney in Washington and speak to them. Let them know that you would like to clear this up. It may be more cost effective to do it now then to be stopped, arrested and extradited. I wish you the best.
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It is certainly possible that you could be extradited. As for how likely it is, that depends on a variety of circumstances. Based on what you've described, I'd say probably not. However, I do suggest that you deal with this sooner rather than later. My advice is to call a few WA DUI attorneys and explain the situation to them in detail. They also should be able to give you more specific advice about the chances of being extradited. Best of luck.
Most states will not take on the expense to extradite someone for a non-felony matter, especially when the crime doesn't involve a specific victim. That being said, you don't want to find yourself in a situation where another state hauls you in and holds you while they wait for WA to make a decision. The best option is to get this all cleared up with the assistance of an experienced DUI attorney in WA. Use this website to find some excellent candidates and make some phone calls to them for possible representation.