There most definitely are. Fanfiction writers are very creative and they like to put the characters in all kinds of situations that are not necessarily in the original books. Harry Potter ice skating could be part of a story where he is on a holiday in a wizarding town with an ice rink, or it could be part of a magical competition that combines magic and ice skating skills.
It could be quite an interesting experience. They might be surprised at the different interpretations of their relationships and stories. For example, Viktor might be amused by how some fanfictions exaggerate his charm. Yuri could be either flattered or a bit embarrassed by how his insecurities are explored in some fictions.
A common theme could be the adaptation of the characters to a new activity. Since they are from a world of battles and magic, ice skating is something completely different for them.
There could be a fanfiction where Yuri is kidnapped for ransom. The kidnappers target him because of his fame and the wealth associated with his skating career. His family and friends are distraught but soon gather resources and work with the police to try and rescue him. They face many challenges along the way, like deciphering the kidnappers' demands and finding their hideout.
It could lead to some self - awareness. Yuri might become more confident if he reads fanfictions that focus on his growth. Viktor could get new ideas for his coaching. Overall, it might strengthen their relationships as they see how fans view their bond.