Yes, a wah wah pedal is an effects pedal, not a musical instrument. I don't know why you think it might be.
I don't know what you mean by “passive” but you're not using the word in an electronic sense. All effects pedals use active electronics, not passive electronics. That's why they need either a battery to power it or a power supply. The only exception I can think of is most volume pedals which are passive but can be used to produce a swell effect (sometimes called “violining”)
Added, regarding your update, your use of “passive” doesn't apply to effects pedals. A wah wah pedal is “active”. A (standard) volume pedal requires exactly the same action but is passive.
I see the distinction you're making between just switching on an effect and having to move something to produce an effect. Lots of effects pedals allow an expression pedal to be connected allowing one of the parameters to be controlled by moving a pedal up and down. That's exactly what is happening with a wah wah - the pedal controls the range of frequencies being boosted. You can use one without moving the pedal (that's the sound of the guitar on Money for Nothing) but most people want the sound of the pedal being moved up and down, most people don't particularly want the sound of, say, the speed or depth of a phaser being controlled by a pedal.