What about if you work for a different company but fly the same type? Would an easyJet A319 captain introduce himself to the cabin crew on a BA A319 as a matter of politeness/safety etc.?
No, only in the case of crews from the same base (not even the same airline if it is big). Anyway it is a Hollywood myth that the crew needs the help of passengers so crews worry much less about this question than anxious passengers.
Most of the time the remaining pilot will land on their own with a little help from cabin crew if needed; if there is a known company pilot on board he or she will help out but there will be no search of the cabin for passengers with some sort of qualification. And in the rare cases of double incapacitation that I can think of the passengers were also incapacitated so no help was possible (Helios, the Payne Stewart bizjet and so on).