Unless you are experienced in repairing cameras, I strongly encourage you to *not* put a tool on that lens. I have repaired many cameras and a number of lenses over the past 20 or so years, and have acquired the necessary tools and skills for this kind of work. And I have an advantage over most folks: As a child, I repaired clocks and even watches for the fun of it. I collect cameras, and I can immediately tell when an inexperienced person attempted a repair, as it's almost impossible to avoid damaging the equipment if you're not experienced. So I strongly recommend that you either live with the fungus, or pay somebody to clean it.
That said, I note that most prime lenses consist of a front group and rear group, with the aperture between them. Often, but not always, one of these groups can simply be unscrewed by hand without employing a tool. Since your fungus is near the middle, you might try unscrewing either group, which would give you access to both inner surfaces, allowing you to clean them.
Mark Overton