Try using your wah pedal more like a 'filter' than a full on 'back and forth' effect all the time.

One idea is to play any ascending/descending run while 'following' the motion with the wah('toe up' at the start of a scale and gradually sweep forward to 'toe down' as the scale goes up for example.)

it will become less of a strong 'wah-wah' sound and a more phase like 'whhooooaaaaeeee' sound.Just try it!