If Kirk were genderbent or sex-changed, some stories wouldn't change at all. "The Doomsday Machine," same. "The Ultimate Computer," ditto.
Some stories of course would change, chiefly those where Kirk gets romantically involved. However, most could be altered with only minor tweaks and sex, pronoun swapping, etc. No big deal, really.
Probably the biggest change would be to "The Paradise Syndrome." Even in this case, the straightforward path to adaptation suggests itself, but it actually adds some interesting twists. Instead of marrying Miramanee and fathering a child with her, Kirk could instead become her rival and marry the medicine man in her place. Kirk herself becoming pregnant and then losing the child herself would radically alter the story.