How should one deal with something that exits after urination, resembles urine, leaves no trace on clothing, and sometimes exits repeatedly?

The whisperings (waswas) have reached a great extent with you. The only cure for your condition is to completely ignore them and pay no attention to them. The feeling you experience of something like urine exiting, without any trace of it on your clothes, is a delusion, and you must deal with it by completely ignoring it. Do not rule that something has exited unless you have absolute certainty that you can swear by, for the default is that nothing has exited without such certainty. Madhiy (pre-seminal fluid) is different from urine; it is a viscous liquid that usually exits after arousal and is discharged intentionally and intermittently.