Wacom tablet pen clicking when it shouldn't

Yesterday, the Bamboo tablet that's worked fine for years suddenly developed a critical problem: simply hovering the pen above the tablet causes a click after a second or so. This makes the device basically impossible to use, but fortunately I have a wireless mouse around for back-up. Some research reveals that the issue is probably caused by the pressure sensor in the pen being somehow stuck or out of position. Removing the tip with tweezers and blowing any dust out has worked for other people, so I will try that when I find tweezers or some other instrument that can remove the pen tip.