I never actually knew about the sticker thing!
We've been bringing our baby's birth certificate and it's been fine. The first time we travelled, I took the initiative to give it to them (we had no idea if we had to show it to them or not); the second time, they didn't ask for it; so the third time, we didn't bother bringing it and they asked for it! But, they just let him through anyway (not on visitor visa). It MAY be because I'm a permanent HKID card holder and they figured my child would have right of abode anyway...? No idea... But, anyway, my point is, I think if you don't manage to get the sticker done in time, you can show them the birth cert... ;P