Student caught cheating when leaving class after handing me the exam Usually I am quite clear that cheating and plagiarism are unacceptable. Although every semester I have to deal with several cases of plagiarism, I had not expected students to brazenly cheat in exams. A few seconds after one student handed me the exam, as she was leaving, I noticed that she had written answers on her hand. She was showing it off to a classmate and laughing as they left. In my country, just writing anything on the hands or anywhere they can read (including the table) is usually considered cheating. Students can check their answers when they are given their corrected exams back. 

I know I could have created a scene on the spot, prevented the student from getting out as she was leaving the classroom, provided evidence of cheating, and graded her exam as 0. But other students were handing me their exams at the same moment, and many others were still writing down their answers. That would surely cause a commotion. I was paralyzed and did not know how to react. I am still not sure how I should have reacted, or how I ought to react in the future. I feel being aquiescent may have an impact on other students' behavior, and also on my feeling of self-respect.

Now I'm facing a dilemma. The student was not caught in flagrante delicto. The evidence for cheating is also gone. If it matters, the student's grade wasn't great either (4,8/10). I cannot decide myself between leaving the issue alone and forgetting about it, grading the student more severely in the next exams, or somehow lowering the student's grade (the last option is a little risky as the student could denounce me).
Exact rules will depend on where you are.  But normally the student has due process rights: to be confronted with the evidence of her cheating, and to appeal to some higher administrator or body if she desires.    Two of your options (grade more harshly / secretly lower grade) are things that you would do unilaterally, without the student's knowledge, and without giving her the right to challenge.  In my view, these options are therefore totally inappropriate and unethical.

The evidence against her is your testimony about what you observed.  If you think this would be sufficient evidence under your university's rules, then it is appropriate to pursue formal punishment as the rules dictate.  If you don't think it's sufficient, then do nothing, and let the student complete the rest of the course without prejudice. (Though of course you can watch her more closely in the future, and perhaps institute procedures to deter this kind of behavior in general.)