Yes, TPE <> HKG the cheapest CM/CS fare available is V class but HKG <> TPE only L class on CX.com.
It really depends on OP's company travel policy.
e.g. my company does not allow Jr. managerial grade staff to travel in Business class but all Economy Class booked must be flexible & sometimes discounted Business class is even cheaper than Y but my company's rules & procedure & Admiration Dept. do not allow it! Good luck.