There are plenty of ways an adept could theoretically "not even know it", but they don't make sense for Batman, who after all didn't fall off the turnip truck yesterday. I could see it if you were porting Shadowrun rules into the Batman universe, but I don't see it if you have Batman in the Shadowrun universe, where the existence of magic is well known.
Adept is the only way you can really go if you give Batman the same attitude about keeping himself "pure", since magic is not really something you can choose to have outside of the metagame of character creation. Hell, if you run with some of Frank Miller's imagery, you could easily give him a bat-aspected mentor spirit of something like Dragonslayer or Wise Warrior.
The trouble with an unaugmented mundane is that Shadowrun has hard limits that such builds smack into. In the comic books, if Batman ran into five or six cybernetic thugs, he would kick the crap out of them, because he's just that damn good. In Shadowrun, his Agility caps out at 7, as does his skill, so assuming a specialization, he is rolling 16 dice for his asskicking. Good, but there are starting augmented or magical builds that could absolutely own him in combat. Yeah, you could give him a suit that is the equivalent of military armor with far less bulk but all of the special accessories, and lots of nasty chemicals in his trusty utility belt, but ol' Bruce never seemed to rely on that stuff - it supplemented his superhuman natural skill.