Well, that was an exercise in frustration.
All I could find was:
CFSCE Standing Orders - http://cfsce.kingston.mil.ca/files/SOP's/STANDING%20ORDERS.doc (DWAN link)
310. DRESS
310.1 The dress of all military personnel at CFSCE shall be in accordance with Canadian Forces Dress Regulations and shall be of high standard. Authorised orders of dress and permissible seasonal variations are contained in CFSCE Routine Orders.
All of the CFSCE SOPS are "under revision" and not published.
Only the most recent edition of CFSCE Weekly Routine Orders and CFSCE Routine Orders (why they have two, I have no idea) are published to the DWAN, and there are no dress issues addressed in them.
Now, a casual survey of other units in all three elements show a smattering of approving authorities from the CO down to the Regulating Chief (in that case, at CFNES would be a PO1/CPO2 in charge of student administration). CFNOS requires the Div Cdr's approval, which is at the LCdr level. MARCORDS say CO/Commandant. That's pretty meaningless info to this discussion, but there it is.
Regardless, the memo you submitted, if it was submitted to the Tp WO, should have been delivered to the Tp WO with minutes attached by those below him/her in the CoC. Only then should it be returned to you after the Tp WO has approved or denied the request. That's basic military correspondence 101, and doesn't matter where you are or what unit you're in.
Sorry I couldn't be of more help. If CFSCE has an established policy for requesting to cease shaving, they've done a pretty poor job of publishing it to the masses.
In general, I find locating Army policies akin to pulling out my fingernails with my Leatherman.