I'm not sure they would operate on the same procedures as Klingon ships. I recall quite distinctly an episode of DS9 where Worf was serving on General Martok's ship and General Martok was refusing to enter Dominion territory to retrieve a damaged Klingon ship and it's survivors. If you don't recall the episode, Worf called Martok a coward and challenged him right then and there for the captaincy of hi ship. Martok won the fight and was so invigorated by classic Klingon combat that he pushed his newly moralized men into Dominion territory, into the ambush he knew was waiting for them and out the other side victorious.
Now imagine that same situation, but replace Martok with an orion female. Do you really see her rising with hot blood and righteous anger at the accusations of cowardice being leveled at her by her first officer? Do you really see her giving him a fair fight? No, it wouldn't work.
I have a female Orion captain. Due to her background, having been adopted into a Klingon house, her outlook is just a bit more Klingon. While she wouldn't necessarily relish a fight, she would at least understand it and respond appropriately. She does have her own version of honor.
But she doesn't have to command by the 'Law of the Jungle'. You know why? Because she's still a full-blooded Orion female, and a right canny one. A good part of her crew is either in love with her or infatuated with her, and she knows it. They are all bent to her will one way or the other. Her biggest problem is really preventing her male crew from fighting over her (which is one reason why she does not allow herself to have relations with any of them). Few of them would actually challenge her, and those that would are either quietly transferred to other ships or taken care of by the rest of her crew.
The only thing she'd ever have to fear is another Orion female. You can be sure that she does NOT allow any other Orion women on her ship!