Why do you need to take the CPU out of the socket just clean it in situ?
Just clean the old TIM off, take your time and watch what your doing. While your there you may as well give everything a light brush with a 2" paint brush > fans, mobo and clean any dust filters.
Them with a can of compressed air or buy a small 240v air bed inflatable pump they cost about £12 a blast of air to remove any dust.
Remember to turn off your PSU there is usually a small switch at the rear of the case. Leave it plugged in if you can so its earthed to prevent any damage from static electricity.
Then press the power button this will discharge ay electricity left in the mobo before you begin to do anything inside the case.