When removing your pickups or doing any work on your instrument I always remove the strings before doing anything. This will help the pickups, switches and coils from getting snagged on the strings. So many rewinds I do are from anxious players or repairman trying to change pickups without removing the strings. This also helps keep the switches from scraping the finish and screws from the pickups from gouging the wood and finish too. If you do this, you will have a better success rate at working on your instrument without other problems to deal with.