They could have a stand-in (kiss-in) do all his kissing scenes. Of course, that would mean we’d only see the back of Kirk’s character’s head while he is kissing.
Sometimes we read the article - his wife DID work as a stand in for the kissing scene. ;^)
They could also sneak in a shot of him kissing a dummie, so his face — but not the dummie’s — would be visible.
(It could happen!)