There is actually only one terminal in HKG in terms of flights, but two terminals for checking in. T2 is just a separate check-in area on the other side of the railway line, it has its own security in the basement, and then a mini transit which takes you the very short distance back under the railway line to T1.

If you can go hand baggage only, it's just like any other airside transfer in HKG, so my advice would be to do that, you arrive in T1 and depart from T1, there is no other terminal at that point. The reason being that the landside walk isn't 10 minutes, but you'd have to enter HKG and leave again, and if you can't use the passport e-gates then immigration and emigration can easily take 30 minutes to do that alone.

On separate tickets this is a dangerous strategy, unless you're ok with the risk and prepared to buy new tickets. You can buy BA + HK Express tickets in one PNR, I think that might even be available via the Contact Centre, and that would protect you. Clearly if you are mixing redemptions and revenue tickets that can't be done on one PNR.