The general rule for a fight involving short blades and no armor is that everyone involved is going to get sliced up, one way or another. As PipperChip said, knife fights are ugly.
Knives have low reach, but move very fast. A scared person with a knife is going to flail with it. That doesn't require any competence on their part, but it makes a dangerous and unpredictable defense, even against a skilled fighter with a comparable weapon. Without escape, placation, or outside assistance as options, I suspect these suitors are going to have a very bad time.
Consider how one might approach a desperate woman with a knife. Actually disarming her is highly risky -- you can mostly forget about fancy maneuvers, this is a death match not a duel, and the moment the suitor makes a grab she's going to instinctively go for his hand. He'll run a high risk of ending up maimed with nothing to show for it. In a frontier culture, infection and disability will be a profoundly scary consequence for a proud, violent young man of marrying years.
What's likely is that, if this custom was somehow set up, the fear of maiming will be worked into the ritual as a disturbing moral lesson. Men who hesitate or make weak grabs will get their hands hacked up, a symbolic castration if you want to get Freudian about it. It might become common wisdom that the best chance for the suitor is to roll the dice on a blind charge, with the hope of scaring or overwhelming his potential "bride" in one go by tackling her before she gets in more than a good slash or two on his raised arms.
If so, it becomes a test of manliness, endurance, and bravery -- and possibly a way for impoverished men of martial talent to advance socially, by forcing marriages with the daughters of wealthy patriarchs. The suitors that live may become a small, mistrusted group of nouveau riche, showing off their scars for years after the event.
Deaths will still be very, very common.