If you use a GPS-log in your debriefing after every dual navex - which I think is a great way to debrief, especially if the track is displayed on a CAA chart - then I would also use it after a solo navex.
For the student, it will feel normal, and part of the general learning experience.
If you use it for a solo navex ONLY, the student might indeed feel uncomfortable or worry about it - not the kind of mindset that will give good performance... they worry enough as it is.
B2N2, the fact that you DID lie and your student MIGHT lie does not justify an instructor lying to their student.