The question should be "I'd like to know what you'll be wearing after the wedding?"
I think the word "finishes" is not necessary since you're already saying that it's after the wedding, it is assumed that the wedding is over.
And for the tense, it should be in future tense "will", because if you say "would (not will) have worn" it's as if you already know that they're not going to the wedding or the activity after the wedding and you're asking them as a "hypothetical question" so to say.
I don't know if I made myself clear S: Hope it helps.
Sorry! I made a mistake and sleahyw is right. If you say "I'd like to know what will you be wearing after the wedding" a question mark is not needed. However, if you want to say it as a question you'd say it like "what will you be wearing after the wedding?"