As you're flying to EDI on BA (and assuming you have status on OW, or a C class ticket) I'd recommend that you head to the terraces lounge in T1 domestic. They have a nice shower suite on the 1st floor at the rear. If you're in J or F you'll get a fast-track card for immigration, I'd suggest you use this and go landside to T1, otherwise go through the Flight Connection Centre and clear immigration there as the queue will probably be shorter.

If you dan't manage to get a Boarding Card in HKG you can either get one in the FCC or the BA lounge. Check out the lines in the FCC and make your decision!

All the above assumes checked through bags.