The only reason we deliberately have new fruit or clothes is because we're saying it anyway on kidush or lighting: if you're (for whatever reason) not saying it on kidush or lighting, there's no reason to have new fruit or clothes. (Of course, if you do have new fruit or clothes, then you say shehecheyanu, same as on any weekday.)
Moreover, saying it at kidush or lighting is saying it for the day: so you only say it one of those two times, not both. But I don't know which one.
(As noted (in a comment on this answer and then in the revised question), Sukos would seem to be an exception because the b'racha is said for the suka as well as for the yom tov (Rama 641), so if a man said it on lighting in his home then he'd repeat it in the suka. Again, I don't know when he should say it. And there may be other, similar exceptions, though I can't think of any.)