Think BIG said “The entire litvish/yeshivish world does not hold hands.”
Think BIG: I’m not sure if you are referring only to the Mitzvah Tantz or not, but many Litvaks do hold hands (including according to Rav Aaron Schecter) between the Chupa and Yichud room. So I don’t see how that would be any more or less a tzinius problem than holding hands at the end of the Mitzvah Tantz. (In fact there are many more non-family members witnessing the hand holding after the Chupa.)
Bottom line is, if done properly there is no tzinius problems in either cases.