Surely the literal translation is 'Kateřina is your woman'. For instance in the context of 'I'm her man and she's my woman'
Not really. While Katerina is your woman sounds ghettoish in English and strongly suggests you are not married, žena when used with a possesive proverb in Czech is married to the subject of the sentence. Žena in those cases can and actually must be translated as "wife". Same goes for man/muž.
Ok. If the man is not married to the woman, but lives with her for years and maybe they even have a child then, Czech: "Ona je tvoje žena (ne manželka).", English: "She is your woman/lady." Of course, the usual "girlfriend-přítelkyně" is probably more used, but is not a rule. So how then?
"tvoje žena" normally means a real wife. If they are not married it is družka, přítelkyně, partnerka,...