I'm doing a campaign with 5 players, and one of them wants to focus on sibling mysteries rather then combat. Since I have quite a few challenging mysteries lined up for them, which the other four would do poorly at, having no ranks in any relevant skills, I said, "Okay. Just wait a while, and I'll see what I can do." We're fine if he ends up with little to no combat capability, since the other four can more than pick up the slack. It's been almost four hours and I'm still staring at the same blank piece of paper. If you guys can think of something, if would great.
Is there any reason why the investigator won't do?
Also, it's generally a bad idea to deliberately make a character that's useless in combat. Every character should have something to contribute in a fight.
+1 to cyrad's comment.
Your player needs a class with a lot of skill ranks like a bard, investigator, or rogue. Each of those can be built with out-of-combat in mind and still be able to contribute when a fight breaks out. You don't need class features to solve mysteries. You need a clever player whose character has some skills to back up the player's intuition. You could use divination spells but I don't think that would be as satisfying.
Pathfinder handles mysteries poorly. Sure, you can still run mysteries but you should not expect the system to help you do it. Quite the opposite, in fact.
You could take a look at Lorefinder from Pelgrane Press. It's an add-on to Pathfinder which sort of tacks on the Gumeshoe system to Pathfinder. Now, I don't think Gumshoe is without fault, but if it's mysteries and investigation it's way, way better than standard Pathfinder.