Are you doing anything in HK? or just using the chauffeur car because it is available?
In my opinion HK immig are the longer wait, than the cross border into china - but i do use shekou (stay in the car during crossing) and lok ma chau (to walk across), i find them cleaner and faster. If you just want to take the car to an immigration facility i believe they can take you directly to lok ma chau station and then you can walk across. On the other side take a taxi to lohu or the metro, taxi won't be expensive.

I would however suggest to forgo the chauffeur and do the ferry crossing, depending on what time you land.

at HKIA i always get a van into town for the chauffeur service and on pickup from hotel they send the S-class. At the airport you have to wait and walk down two levels to the van, and at times there is a wait (no more than 10 minutes).