it's ok to run without the body. we all do it from time to time, some of us more than others. the cars function just fine without them. however, tracks will require you to run a body though. so if you'll be racing on a track in competition you will have to run the body.
you also need to remember the body does more than just give the car it's shape and make it look cool. it also protects the electronics and chassis components from debris and crash damage.
think of not running a body like sending a warrior into battle with no shield.
best thing to do would be to remount the ESC, or re-solder the wires so everything fits correctly. or if you just want to halfass it, clearance the body.