If the bride and groom have insisted on throwing the bouquet and the garter, and the guests have been polite enough to participate, the garter-catcher is expected to place it on the bouquet-catcher's leg and claim a dance. There's a certain pleasant symmetry to it. There's also the potential for trauma.
While the idea of bringing together a pair of sweethearts during this event is romantic, fate can have a wicked sense of humor. The situation is ripe for creepy mismatches. Cousins dancing with cousins. Old flames with enemies. Gawky 15-year olds gartering middle-aged aunts while the other guests laugh and clap. It's probably best to skip it and save everyone the nightmares later.