The fee will be the difference between your purchased fare and the regular business class fare, which is likely to be quite high on the day of departure. No discounted upgrade fees. It may not be possible on a codeshare. The issue is that they have to be able to figure out what the cost of your ticket was so they can up-charge you, and that is likely to be a problem if the ticket was purchased as a codeshare. In fact, my one experience with this was trying for a J->F upgrade on a CX flight on CX stock using a corporate negotiated fare and the HKG staff couldn't figure it out, so it wasn't even an option.