Cleaning the sensor is good for tracking problems and always a good idea to maintain your mouse but from what you are describing with intermittent clicks without touching the button, given it being a corded mouse it could be a break in the wires somewhere within the cord caused from bends or kinks in the cord. You could try to find it and put tape where its at but IMO it is better just to get a new one.
BTB's idea is also very plausible and I would check that 1st
BTW mouse buttons have x amount of clicks before they start having problems so check that when looking at new ones. Some will specify how many others wont. It can be anywhere from 100,000 to 10,000,000 depending on the quality of the mouse.