Parakeets don't stink at all! Well... Budgies don't.
Unless there's something up with them, budgies actually smell quite nice, and their cage doesn't get smelly at all if you keep it clean
But with them you do need to spend a LOT of your time with them, talking to them and bonding with them if you're going to keep one.
To be honest with all birds you want to keep as a pet you need to be there for them to some extent
All birds can be a bit noisy at times, especially when they scream and shout, but their tweeting and songs aren't unbearable.
But if you're looking for something that you can keep as moving wallpaper and not really interact with, try fish!
You're kinda out of luck if you just want a single bird to just look at. They need plenty of love and attention.
It's like asking if you could find a tiny child that makes no noise that you don't really have to be hands on with. And that wouldn't work.
Not trying to offend or anything.