Your manager’s fear of looking bad to his boss reflects his inexperience. (Or a dysfunctional organization, but let’s hope that’s not true.) It’s your skip’s job to provide mentoring to a new manager, and to support him in creating a high-performing team, which includes guiding him through using the company’s performance management process to take care of underperforming employees like your toxic coworker.
Since you have a good relationship with your skip, I think a frank conversation about the effect this person is having on the team will go well. You can also share that you’re worried about it blowing back on you, and your manager’s fear of looking bad. If your skip is smart, he’ll use that opportunity to take a more active hand in mentoring your manager without bringing your name into it.