Pretty difficult requirements. Just a few thoughts from someone who has shot powder and air. First and foremost, give up on worrying what you look like or what others may think. I have a neighbor who used to laugh at my Hatsan rifle. I heard all the "not a real gun" BS. I asked him to come over and shoot some time. He finally accepted and we had a great time. He walked away with an amazed look at the fact that we shot 250 rounds and spent all of $7. Even a .22 PB would have burned through $12 of the cheapest junk ammo. We shot in my yard from my porch. No range needed. I set up a couple Field Targets and we just blasted away all afternoon, only stopping to refill the airtank. He asked me how often did I shoot? I told him at least once a week. He shoots about 2 times a year! Long and short of it- Guess who is looking into picking up and airgun? When I showed him my indoor range for pistol use he was so green! He hunts with his pistol, but can only afford to "practice" once a year. He has a barn that he could easily set up a 10 meters range.
The point here is give up on image. As for accuracy, well I would probably avoid the CO2 BB pistols. Fun to shoot as plinkers, but accuracy is usually measured in the ability to hit a time can. For true accuracy look to many of the great recommendations already presented. My personal favorite is the Crosman 1701P. Hole in hole when I do my part. This gun has a $30 moderator on it that makes it ultra quiet. I shoot it indoors all winter long and the family never even hears me.
So I understand what you are looking for, but t just may not be possible to the degree you seek. Lowering your requirements may just give you a fun, satisfying shooting experience.