Li Shenron
Legend
Handwave it. Give 'em what skills, tools, etc make sense and shine it.
Sure, but notice how my idea is actually very close to handwaving it!
I don't really do any work beforehand. What I really do, is just open up Basic at the page of the relevant background. So if the PC are talking to a guard, I'll keep the Soldier background in front of me, if they're talking to the librarian I'll keep the Sage background in front of me, if they casually meet and start a conversation with someone in the street, I'll keep the Folk / Noble / Criminal page in front of me (you never know who you meet on the street...

Everything is already there. At most, I replace one skill on the spot.
But really all this happens in real time, I am not preparing anything before. The nice of this, is that whatever the PC decide to bring up in the conversation, there is stuff on that page that helps me improvise something interesting: I can roll on the trait (or ideal/flaw/bond) table to determine the general attitude and response of the NPC, I can use the listed proficiencies + a random background sub-choice to determine what are in general the things this NPC know if they ask him questions.
Ability scores are indeed mostly irrelevant, until there is to roll some dice I can totally ignore them. They are just an addition, but it takes 3 seconds to decide that NPC Joe is strong but dumb, and NPC Mary is wise but shy.