To hunt unclassified wildlife, you need a valid big game or small game license. You can hunt unclassified wildlife year round with no bag limit and with any weapon. For instance, you can legally hunt unclassified wildlife with an air rifle.
Attached below is the Small Game, Furbearers, and Unclassified Species section (Pages 151-152) from the 2015-2021 Game Management Plan available online at http://wdfw.wa.gov/publications/01676/wdfw01676.pdf.
20th of March, 2015