Cleaning with alkaline solution (pH~13) will remove the oxides of tungsten. Immerse the tungsten fiber in 0.1 M NaOH solution (20 ml of solution per cm2 of exposed surface area of W) for about 20 s or so (I do not know the size of your fiber, you have to decide on the time of immersion - if you see a violent reaction then take the fiber out immediately!), then wash with plenty of DI water followed by washing with alcohol and dry in nitrogen stream. Acid treatment will give you surface oxide on W.
Another option for cleaning tungsten, if you do not want to mess with chemistry and you have a vacuum oven:
just heat the tungsten fibers in vacuum to 1000°C and the surface will be completely clean (you must remove the fibers from the furnace only after complete cooling).