Days Gone. It's basically a biker road movie set in a zombie apocalypse scenario playing out in rural Oregon. Strong story, beautiful graphics, and a healthy balance between scavenging/exploration and fighting.

If that's still too violent, maybe the Hitman series. That's basically 95% exploration / problem solving because you have to spend most of your time figuring out how to get close enough to your target so you can eliminate them without causing too much of a stir.

Also Deus Ex Human Revolution or Mankind Divided, for similar reasons. You're pretty much always outnumbered and outgunned so you have figure out how to get around and complete your objectives without being detected and only pick your fights sparingly.