The 'him' could also be Sirius Black. For example, in a tight escape from some dark wizards in a narrow alley, Harry and Sirius have to squeeze through a small passageway. In the process, they are rubbing against each other. This could be a tense and exciting moment in the fanfiction, highlighting their family - like connection and Sirius' protective nature towards Harry.
The 'him' could be Draco Malfoy. It would create an interesting dynamic as they are usually rivals. Maybe in a situation where they are forced to work together on a secret mission for the wizarding world, and they end up in close quarters, rubbing against each other accidentally. This could lead to a change in their relationship, from enmity to a more complex understanding.
One possible plot could be that in a magical accident, Harry Potter finds himself in a situation where he has to constantly be in close physical proximity to another character, like Ron. Maybe they are stuck in a shrinking charm situation and have to rub against each other to stay warm in a cold, magical environment. This could lead to some humorous and heart - warming conversations as they deal with this strange situation together.
'Him' could be a centaur. In the Harry Potter universe, centaurs are intelligent and powerful beings. Harry might ride a centaur in a situation where he needs to quickly cross the forest and the centaur's speed and knowledge of the terrain would be very useful.
The 'him' could also be Snape. In a fanfiction, a spell or a magical experiment could go awry and force Harry to touch Snape. Given their complex relationship in the original series, this forced touch could be a catalyst for a lot of emotions. Harry might finally understand some of Snape's motives or Snape might have a moment of vulnerability that changes how he views Harry.
It could be Voldemort in a really strange and dark fanfiction concept. Maybe Voldemort has found a way to magically force Harry to perform this action as a form of humiliation and domination. This would be a very different take on their relationship compared to the original series.
He could use his wandless magic. Harry has shown some ability for wandless magic before. He might use it to unlock the doors or create distractions to escape. For instance, he could make a loud noise to draw the Muggles away from the exit and then make a run for it.
One possible plot could be that a dark wizard has somehow magically compelled Harry Potter to perform this action against his will. However, this goes against the core values of the original series, so it would be a very dark and twisted fanfiction. It might involve Harry having to fight against the magical compulsion through his own inner strength and the help of his friends.
Maybe it's a magical portrait in Hogwarts. Some portraits in Hogwarts have a lot of knowledge and wisdom. One particular portrait of a former great wizard could notice Harry's need to fly without a broom. This portrait could then guide Harry through a series of magical trials and lessons, teaching him how to tap into his inner magic and fly without the aid of a broom. It would be a long and difficult process, but Harry, being determined, would eventually master it.
Luna Lovegood might also be a likely candidate. She has a unique perspective on the wizarding world and is not bound by the traditional views. Luna could offer her creativity and her ability to see things that others overlook. Her friendship with Harry could easily lead her to support his new grey faction and contribute in her own strange but wonderful way.
Hermione could still be a great ally. She's smart and observant, so she'd probably be able to figure out ways to communicate with Harry even if he's mute. Also, Hagrid. Hagrid has a big heart and he would see past Harry's inability to speak. He would likely take Harry under his wing just like in the original story.
The Weasley twins might also get involved. They are known for their love of pranks and inventing new magical items. They could create a special device or a new type of magical makeup that Harry could use to change his appearance. They would probably do it with a sense of humor, but it could still be an effective way for Harry to transform himself, like giving him a false nose that can be changed at will or a set of robes that alters his body shape.