You don't have many sectors where F is currently available.

CX have removed F from a lot of their regional routes, HKG-NRT, HKG-BKK & SIN-BKK for example.

They still seem to fly F on some CGK, SIN, ICN & KIX flights. However the way CX keep shuffling their schedules and remove and restore F to regional routes it is a game of russian roulette.

Also SIN-NRT does not currently run with F on JL although this may be seasonal. Ditto NRT-DEL.

Are you looking to maximise points / miles as well? You may be able to get some more value out of your NA portion of the trip if you wanted to.