The Rambam says in Laws of Talmud Torah, Chapter 4, Law 5
"However, if it appears to the teacher that they are not applying themselves to the words of Torah and are lax about them, and, therefore, do not understand, he is obligated to display anger towards them and shame them with his words, to sharpen their powers of concentration. In this context, our Sages said: "Cast fear into the students.">
The Rambam also says in Hilchot Rotzeach and Shimirat Hanefesh Chapter 5, Law 6:
Similarly, when a teacher strikes a student or an emissary of the court strikes a litigant who refuses to appear in courtand accidentally kills him, he is not liable for exile.
This concept is derived from Deuteronomy 19:5, which mentions the punishment of exile for a person who unintentionally kills a colleague while "chopping wood" - i.e., a permitted act. Thus, this punishment is not imposed when a father strikes a son, a teacher strikes a student, or an emissary of the court strikes a litigant, for they unintentionally killed while performing a mitzvah.
It would seem from the Rambam that a Rebbe has license to motivate the student with even means such as embarrassment or even striking the student. If the student is being lax in his studies and sleeping I think it is a fair deduction that if a Rebbe could actually embarrass or strike them that he could gently wake them up and encourage them to learn. Perhaps in todays world methods of striking and embarrassment may be looked down upon. In fact a Rebbe would probably lose their job. However, in a strict Halachik sense, which the questioner poses the question, I don't see why Gezel Shina would be worse than the above mentioned methods.
I vaguely recall a Law that they can tear the garment of Cohen to educate him if he is being lax or negligent. I don't remember the source for this, so I mention it in passing. However, this would be another support that Gezzel Mamon would not be a problem to educate. I would think that would apply to Gezzel Shinah.
I remember my teacher causing whiplash whenever a classmate would put their head down to sleep. It is a new day and age now...