I find the idea of an playing ex-spaceship's computer who occasionally calls people "Dave" inappropriately and has "the greatest possible enthusiasm for the mission" hilarious. It would have the Piloting Origin quality from Runner's Companion, of course, and would primarily be a rigger, possibly with a splash of hacking. Would such a character work, and what might its skill and attribute layouts look like?

Very hilarious, indeed. It probalby has a nice charisma and some intuition for rigging. And lots of willpower for staying stone cold at all times. Give it less hacking skills, but lots of vehicle skills. Add a good measure of influence or just specialize in etiquette and negotiation. And don't forget empathy software for saying "I am sensing a high stress pattern, Dave. Maybe you should sit down, take a stress pill, and think things over."
And don't forget to promise cake for cooperation.

And believe me, it is still alive...

Hands up who else does love Papa Lazarou?