Designing a credit-by-examination exam
There is a lot missing information here that makes it difficult to provide an fully informed response. For example, the subject, whether this is a theoretical or application class, the way it is taught, the number of topics, the scope and sequence etc. 

At many universities, credit by examination is only possible if the student wants to prove that they already have mastery of the subject. In other words, unless the student is completely lying, they should already be highly familiar with the content of this subject and the simply want to prove that they already know it. 

If the current final exam is comprehensive in nature it should be suitably for credit by exam, regardless of one's philosophical position. The reasoning being is that the student needs to demonstrate mastery of the entire subject and not just a portion of it. If the current final exam is not comprehensive, mixing it with the mid-term should help to develop a comprehensive exam.