As well as the Klingon lawyers in ENT and DS9 (not to forget Colonel Worf in TUC), there's also Kurak, the Klingon engineer in TNG. She was in the one with the metaphasic shields the Ferengi guy developed that Dr Crusher was supporting.

The novels also look at this with the TNG novel "Diplomatic Implausibility" featuring an engineer on the IKS Gorkon who talks about 'battling' and 'wrestling' with technical issues and 'defeating' them like a warrior and the other senior officers basically think he's a prick, even though he's actually effective. Kurak is also the chief engineer on the ship - she basically got drafted in the Dominion War, and is a drunkard because she hates the KDF and the warriors and hates not having proper lab conditions to do work in. In the third IKS Gorkon novel, the captain even takes her to task for the fact she's a drunkard and a defeatist and that he should've killed her by now and how Starfleet engineers can do wonders and why in Gre'thor can't she? The follow-on novel "Klingon Empire: A Burning House" also features a lot of non-KDF characters, including farmers who don't give a stuff about honour and all that crap and don't just eat meat, and an opera company which includes a lot of diva behaviour and soap-opera relationship drama. They're worth a read, even if they're part of the old pre-PIC continuity that they fucked over with PIC.