won't that damage the board tracks?
No, it will damage mostly everything it touches, plastics and whatnot.
Screwdriver, water, soap, hairdrier. Used it on that exact switch as well as many others(when I was into PC overclocking I used to clean a lot of electronics this way and never damaged one). Take it off the car, dissasemble it properly, wash all the parts in the sink with water and soap, dry with hairdrier or left in the sun for 1 hour, assemble back and voila.
Although, if the button pushes properly and makes a click, it might be some other fault. A friend of mine had that exact problem a week ago and changed 3 botton asemblies, the part with 3 buttons and LEDs and all that, but fault was somewhere else, sorted in the meantime but I have no idea where the fault was, will ask.