Remember that you are free to make up words in your fiction as long as you provide the meaning. Maybe in the universe you're writing they use different words.
You can use animals to reference how they are on the hunt, and pick an animal that fits your kitsune character.
Foxes are omnivores. They eat fruit, bugs, meat, eggs, etc. This can be interesting in the culture of your new world where kitsune exist, and people would have slang words dating back hundreds of years. Let's pick what females are biologically wired to do, producing eggs (ovum). A female kitsune who goes after many women could be called an egg-stealer since she keeps them to herself, thus preventing pregnancy and so the 'stealer' would come into play.
We can play a little with languages here. Kitsune is a Japanese word meaning fox. In the shinto folklore, a zenko is a good, proper fox that serves Inari (goddess). A yako, on the other hand, is a mischievous fox that plays pranks on people, like possessing men and doing their wives who later have the fox' children. With this, you can use the world Yako to refer to the sexual expression of a female kitsune who goes after many women in order to form long-lasting relationships. (Why would the word Kitsune exist if Japanese doesn't?) You would have to explain to the readers what the word means, easily in a single line.
Hope it helps =)!