Let me define my terms.

By “no combat” I mean a campaign where we never use any combat-specific mechanics. There may well be chases and sneaking and races against the clock, and lots of social interactions, and all of that. We might import the battle of the bands mechanics from the Fate Core supplement Rockalypse. But characters will never be trying to injure or kill others, and they will not face opponents dishing out attacks intended to injure or kill them. (I used to think that this would be obvious. I also used to think people wouldn’t answer a question about no-gore horror movies with Alien and Hellraiser. Sometimes the world lets me down.)
With that constraint, what does Savage Worlds bring to our table? Are there enough skulls and edges to allow for differentiated characters and NPCs? How are the various companion books for genre-specific support? Any plot point campaigns that could work with this, or so they all call for some bloodshed?
Thanks in advance, all of you with experience!
(There also are low-but-not-zero combat options that interest me, but experience tells me if I don’t obviously focus on zero combat first, I never get useful answers about it. Gotta absolutely nail down my right flank before advancing.)