None? I mean…they’re super-heroes. They’re all unrealistic.
The Punisher is about as “realistic” as it gets, but, as you say, it’s fantastically unlikely he’d survive more than a couple of months. Batman’s got nothing on the Punisher’s plot armor. He’s also got an infallible ability to identify criminals - Ghost Rider’s got nothing on him there. He literally never kills the wrong person. Innocent people don’t even ever get caught up in the crossfire, or hit by a stray round, or a ricochet, or a round that over-penetrated, or…
There have been throwaway vigilante characters in various “deconstructed” super-hero stories who get themselves killed almost immediately. That’s probably about as “realistic” as you’re going to get.
In the real world, no amount of training and gear makes you invulnerable. You can make the optimal decision in every single situation, and still get killed by dumb luck.
And literally every “normal” vigilante has completely unrealistic skills and abilities, because they’re not real vigilantes, they’re action heroes. If you rule out Green Arrow for being unrealistically good with a bow, no one is realistic.
With all of that being said…
Maybe Oracle? Barbara Gordon, in the continuity where she was paralyzed from the waist down and retired her Batgirl identity, became a computer hacker who aided and guided other heroes remotely. Of course, computer hacking doesn’t actually work like it does in the comics, but the basic idea of a computer hacker who uncovers wrongdoing and anonymously guides others to take down the bad guys is at least vaguely plausible, and to some extent actually happens in the real world.