Unfortunately, loans aren't real to most people until after they've had to climb out of debt, and the most useful time to know is before you're in debt in the first place.
Nobody parses the rates to figure out what they're actually PAYING for these loans, and few realize minimum payments are a lifetime of debt. "I want to live today" is not as strong when it realizes "I want to not mortgage the rest of my life to debtors" requires a little delayed gratification.
The most terrible thing credit managed to do to us was convince us you could "Live today" on borrowed money.
You won't reach her if you talk to her as a corrective intervention. Most people who oppose these conversations say it's not your business. Those who support intervening think it's kind of you to take some initiative to help someone in need. It has to be a calm conversation. Ask permission. "Hey, I wanted to talk to you about a concern for a minute. Is that ok?" Tell her you that you just wanted to leave her a little bit of information, not give her a lecture, because you hope for her future happiness. Give the VERY MOST SUCCINCT and neutral argument for not being in debt you can find. "Once these come due, they can be more difficult than they seemed at first. Paying the minimum is usually not effective unless you have a great rate. You can rack up enough debt to be unable to pay it, which could hurt your credit, which would hurt your ability to rent, buy a house, or get a car. If your loan balance is high enough that the rate creates your minimum payment, you may not make progress on it, or you may feel unhappy about your progress." Give a few examples if she seems engaged or curious - SHORT ones. Offer, if she wants help combing through loan terms to make sure the cosigning won't create problems, you would be happy to volunteer, but leave it at that. Offer that she can contact you later if she has any questions and wish her the best. Then let it go.
Your challenge with your wife will be explaining you don't want to win, to be right, or to control the girl, you just don't want to know somebody tried to talk to her about this and gave her the chance. You may, because it's not YOUR niece, just have to ask your wife or her sister to have this conversation to preserve relationships. Explain what you plan to say. Promise you just want one shot to explain it and you'll leave it alone. I assume we're talking about an adult, but doing this against your wife's wishes, and especially against the student's mother's, may be a bad idea. If ultimately you decide not to do much, you could still say "hey, if you ever wanted to talk about student loans and finance, I know it can be tricky, and I wanted to leave you an open invitation."
Your best result probably won't be immediate. If the girl does NOT feel pressured by you, she may call you a week or a month later to ask you a question and engage you further. Don't gush if this happens - just use the same neutral tone to answer to the best of your ability.