Would be very grateful for any advice with my slight problem below!

I will be travelling with my wife and child from LHR-ICN-HKG tomorrow on BA and then CX on two separate PNRs. I was planning to check in and print all the baording passes and just stay airside in ICN. However, I have just checked in for all my flights but on the CX website, from ICN-HKG, I have been asked to pick my boarding pass up at ICN at the self check in counter as online printing is not allowed for that particular departure. However, with a small child I would much rather prefer to remain in transit having arrived from LHR. Is there anyway to pick my boarding pass up in the transit area rather than exiting through customs going landside and coming back through again?

Thanks in advance for any advice!