Aside from the chatan, the main person who needs to know about a chuppat niddah is the mesader kiddushin, the officiating rabbi. Chuppot niddah happen often enough that rabbis are unfazed by them. By knowing the situation, the rabbi can help ensure that adjustments to the wedding are as discreet as possible.
As usual during niddah, the couple will need to observe harchakot. At the ceremony, this leads to some minor changes.
Though a husband is usually not allowed to hand anything directly to his wife while she is in niddah, the couple are not yet husband and wife prior to kiddushin. Therefore, many halachic authorities permit the chatan to place the ring directly on the kallah’s finger, as long as he takes care not to touch her while doing so. In some cases, the rabbi may advise him to place the ring inside her hand instead.
Once the chatan has handed the kallah the ring, the harchakot apply more fully. Therefore, the ketubah should ideally be passed to the kallah via another person, and the chatan should give the cup of wine to the rabbi or the kallah’s mother to hand to the kallah. The chatan should be sure to drink first, because he may not drink from a cup after the kallah has done so.
In the case of a chuppat niddah, the couple should not hold hands at the end of the chuppah. Instead, they might make dancing motions and a kallah might wave a bouquet.
A couple may feel self-conscious about these changes, especially about not holding hands. It can be helpful to bear in mind that guests with the halachic knowledge to discern any differences will also understand that these things sometimes happen, and the couple is simply acting in accordance with halacha. In all likelihood, though, most guests will not notice.