Identifying pop songs by their intro. I’ve played party games that required that skill, and I smashed everybody else.
Perfect pitch, but it’s most accurate on a piano vs other some other instruments.
2 out of 5 people don’t already know how to juggle 3 balls in a cascade enough to keep them in the air for 15 tosses. Maybe they could quickly learn it, but they don’t already have this skill under their belt.
I can probably snatch flies out of the air better than 99 random people. When I was young, I lived in an area with a moderate number of flies and we had no window screens. There was never a fly swatter around when I needed one and the darn things would land far enough away that I couldn’t slap them with my hand. I started just snatching at them. It doesn’t take long to get pretty good at it. It’s a simple skill, similar to throwing a ball, but it seems like not many people even attempt it. I can give some hints about how to be successful at it.
I’ve been married for 13 years and my wife is still surprised/proud/shocked when I do it.
I also do moths that are flying around lights.
Dopers are an elite group, I doubt I can do anything better than any Doper in a 99 Doper club.
Coding, I know the OP says “no work-related skills” but to me is not work-related, I was coding 10 years before I started working!.
If coding is not allowed: GMing a table top RPG game.
Other entries:
Identifying SF short stories/novels (I think I would win unless I had the misfortune of finding @Andy_L or other knowledgeable dopers in the group of 99)
Tolkien Lore: Again, if @Qadgop_the_Mercotan and/or other dopers are not in the competition.
I’d bet that my car could beat you. It amazes me when it chooses what looks like a far too small space and then neatly slots itself in.
Along similar lines, tie a taut-line hitch blindfolded.
Tie a bowline behind my back.
Tie a Christmas Tree to the roof of your car. I set it up so you can pull two strings and the twine just comes free, no cutting!
That reminds me, I used to be unbeatable at rolling a quarter down my nose and having it bounce into a shot glass! 
I have a brain full of random useless facts, which makes me pretty good at trivia. I’ve done a couple trivia nights with my sister and BIL. He is better at trivia than me, but I bet against 99 randos I’d have a good shot at being the top trivia master of the group.
I have kind of a superpower for recognizing voices. When an actor does a commercial voiceover I’m very good at placing the voice. I first realized I had this power when I recognized the voice of Richard Thomas (John-boy on The Waltons) in a commercial. I had not really watched The Waltons at the time, or much of anything else Thomas had been in, yet somehow I knew his voice. This also works when I watch something in which an actor is wearing some makeup, prosthetics or disguise that renders them unrecognizable. I hear their voice and say “hey, that’s (actor name)!”.
Fun thread BTW, hearing Dopers talking about their unique skills.
Drive.
Identifying the illustrators of pulp magazine covers.
Trivia about 1960s Beach/Surf culture
Name that Psychedelic record from 1967
Pinball Machine repair
Conversing in pantomime (making myself understood to someone I don’t share a language with)
I’m a lumberjack, and I’m okay
I sleep all night and I work all day
I can recite all of the English/British monarchs in order starting with William I (the Conqueror).
It’s not a skill I necessarily tried to learn…I just like English history.
Reciting from memory the broadcast rights disclaimer that played on Chicago Cubs Radio in the 1980s and 1990s. “This copyrighted telecast is presented by the authority of the Chicago National League Ball Club…”
Listening to that disclaimer ~100 times per season for over 10 seasons drilled it into my head forever.
My fingers fly over an adding machine!
I’d say stuff like this fails the brain surgery sniff test, having extremely niche knowledge is like being trained in something very specialised.
Off the top of my head: 1) air-layering a woody plant, and 2) picking up a bit of lettuce that’s fallen to the kitchen floor with my toes.
It was worth a shot.
Oh, that reminded me of a household super skill I have: catching cups, glasses, dishes etc. falling from a cupboard before they smash on the ground, with my hands, and if this fails, with my feet. I used to be a soccer goalie, and reflexes were always my forte.