If I were doing this, I would go landside first - that's where the ticketing desk is and where the people who have some clue will be. CX lounge staff are not ticketing people. Once you've talked to the people at the ticketing desk and they are confident they have all they need to get the job done then they will almost certainly suggest you go to the lounge and wait.

Of course if the flight out of HKG that day is one that needs to be rearranged then you won't be able to transit straight to the lounge because you won't have a boarding pass for the onward flight (unless of course you have one for a different flight!). But I wouldn't recommend checking in for a flight that you want to change just to get a boarding pass. And you'd also have issues with checked bags (if any).