Having spent a couple of hours searching the web, the Dell 3rd wire in the charger lead is a data comms wire between the laptop and an IC in the charger. The purpose is to identify the charger, although the cynical side of me suspects it is to discourage the use of 3rd party adapters... I don't know about HP, but suspect it works in a similar manner.
Before I try it, does anyone know if using just a 2 wire connection powers the laptop but doesn't charge the battery? If so, it could be useful as charging with a generic adapter may not be needed when powering from 12V.
FWIW, speaking with Dell Support, they seem to know very little about powering some models of their laptops from a 12 Volt "auto" adapter, even though they sell adapters...
SJ