We talk a lot on this forum about all the wars and battles we can field (in a game called "Only War," shocking I know.)
Regardless what non combat scenarios do you have that may stretch some of those other skills like logic, knowledge or fellowship?
I had the PCs go to a farming community to beg for more supplies and men to help repair the walls that defended them. Once inside the two political parties tried to use the players to get stuff done like low level enforcement and political endorsements both from the IG and threatening others into voting for the right guy. In the end there was a plot twist as to who was drying up the watet burning fields and killing groxes in the night to gain power and the PCs had to discover this.
Some of this led to combat, yes but it still made the players stretch their brains rather than play Call of Duty: 40k edition.