Does swallowing one's saliva after it has reached the outer lip invalidate the fast, whether due to obsessive-compulsive disorder or fear of blame?

The cure for whisperings (waswas) is to ignore them and not pay attention to them, and to disregard the whisperings related to wiping the lips with tissues. What is prohibited is intentionally swallowing saliva after it has exited the mouth. If the saliva reached the throat unintentionally, or if its exiting was merely an illusion and a whispering, then there is no compensatory fast (qada') upon you; otherwise, you must perform a compensatory fast.